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107-404: As shown by Gerard 't Hooft , strong interactions of the standard model, QCD, possess a non-trivial vacuum structure that in principle permits violation of the combined symmetries of charge conjugation and parity , collectively known as CP. Together with effects generated by weak interactions , the effective periodic strong CP-violating term, Θ , appears as a Standard Model input – its value

214-469: A Weyl semimetal material. In the axion insulator phase, the material has an axion-like quasiparticle – an excitation of electrons that behave together as an axion – and its discovery demonstrates the consistency of axion electrodynamics as a description of the interaction of axion-like particles with electromagnetic fields. In this way, the discovery of axion-like quasiparticles in axion insulators provides motivation to use axion electrodynamics to search for

321-428: A wormhole in the early universe, such a wormhole could be stabilized sufficiently to exist in the present day. The exterior geometry of a (straight) cosmic string can be visualized in an embedding diagram as follows: Focusing on the two-dimensional surface perpendicular to the string, its geometry is that of a cone which is obtained by cutting out a wedge of angle δ and gluing together the edges. The angular deficit δ

428-456: A 225-day run to set the best coupling limits to date and exclude some parameters. While Schiff's theorem states that a static nuclear electric dipole moment (EDM) does not produce atomic and molecular EDMs, the axion induces an oscillating nuclear EDM that oscillates at the Larmor frequency . If this nuclear EDM oscillation frequency is in resonance with an external electric field, a precession in

535-415: A book length exposition of his ideas which, according to 't Hooft, has encountered mixed reactions. Cosmic string Cosmic strings are hypothetical 1-dimensional topological defects which may have formed during a symmetry-breaking phase transition in the early universe when the topology of the vacuum manifold associated to this symmetry breaking was not simply connected . Their existence

642-669: A classical definition, whereas the field theory cosmic strings are almost exclusively treated classically. In superstring theory, the role of cosmic strings can be played by the fundamental strings (or F-strings) themselves that define the theory perturbatively , by D-strings which are related to the F-strings by weak-strong or so called S-duality , or higher-dimensional D-, NS- or M-branes that are partially wrapped on compact cycles associated to extra spacetime dimensions so that only one non-compact dimension remains. Cosmic strings, if they exist, would be extremely thin with diameters of

749-400: A conical singularity. However, this static geometry is unstable in the super-critical case (unlike for sub-critical tensions): Small perturbations lead to a dynamical spacetime which expands in axial direction at a constant rate. The 2D exterior is still compact, but the conical singularity can be avoided, and the embedding picture is that of a growing cigar. For even larger tensions (exceeding

856-762: A constitution for its future inhabitants. He is a member of the Royal Netherlands Academy of Arts and Sciences (KNAW) since 1982, where he was made academy professor in 2003. He is also a foreign member of many other science academies, including the French Académie des Sciences , the American National Academy of Sciences and American Academy of Arts and Sciences and the Britain and Ireland based Institute of Physics . 't Hooft has appeared in season 3 of Through

963-482: A dark-matter candidate and a solution to the strong CP problem. If inflation occurs at a low scale and lasts sufficiently long, the axion mass can be as low as 1 peV/ c . There are two distinct scenarios in which the axion field begins its evolution, depending on the following two conditions: Broadly speaking, one of the two possible scenarios outlined in the two following subsections occurs: If both (a) and (b) are satisfied, cosmic inflation selects one patch of

1070-524: A fairly generic prediction in both quantum field theory and string theory models of the early universe . The prototypical example of a field theory with cosmic strings is the Abelian Higgs model . The quantum field theory and string theory cosmic strings are expected to have many properties in common, but more research is needed to determine the precise distinguishing features. The F-strings for instance are fully quantum-mechanical and do not have

1177-530: A galaxy by a straight section of a cosmic string would produce two identical, undistorted images of the galaxy. In 2003 a group led by Mikhail Sazhin reported the accidental discovery of two seemingly identical galaxies very close together in the sky, leading to speculation that a cosmic string had been found. However, observations by the Hubble Space Telescope in January 2005 showed them to be

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1284-484: A kilometer in length may be more massive than the Earth. However general relativity predicts that the gravitational potential of a straight string vanishes: there is no gravitational force on static surrounding matter. The only gravitational effect of a straight cosmic string is a relative deflection of matter (or light) passing the string on opposite sides (a purely topological effect). A closed cosmic string gravitates in

1391-458: A magnetic field. The concept was first put forward in 1986 by Luciano Maiani , Roberto Petronzio and Emilio Zavattini . A rotation claim in 2006 was excluded by an upgraded setup. An optimized search began in 2014. Another technique is so called "light shining through walls", where light passes through an intense magnetic field to convert photons into axions, which then pass through metal and are reconstituted as photons by another magnetic field on

1498-402: A more conventional way. During the expansion of the universe, cosmic strings would form a network of loops, and in the past it was thought that their gravity could have been responsible for the original clumping of matter into galactic superclusters . It is now calculated that their contribution to the structure formation in the universe is less than 10%. The standard model of a cosmic string

1605-556: A new global symmetry (called a Peccei–Quinn (PQ) symmetry ) that becomes spontaneously broken. This results in a new particle, as shown independently by Frank Wilczek and Steven Weinberg , that fills the role of Θ , naturally relaxing the CP-violation parameter to zero. Wilczek named this new hypothesized particle the "axion" after a brand of laundry detergent because it "cleaned up" a problem, while Weinberg called it "the higglet". Weinberg later agreed to adopt Wilczek's name for

1712-533: A pair of similar galaxies, not two images of the same galaxy. A cosmic string would produce a similar duplicate image of fluctuations in the cosmic microwave background , which it was thought might have been detectable by the Planck Surveyor mission. However, a 2013 analysis of data from the Planck mission failed to find any evidence of cosmic strings. A piece of evidence supporting cosmic string theory

1819-408: A possible origin for both phenomena. In 2022 a similar hypothesis was used to constrain the mass of the axion from data of M87*. In 2020, it was proposed that the axion field might actually have influenced the evolution of the early Universe by creating more imbalance between the amounts of matter and antimatter – which possibly resolves the baryon asymmetry problem. In supersymmetric theories

1926-481: A relatively fringe subject at the time because it was thought that these could not be renormalized . His assignment was to study the Adler–Bell–Jackiw anomaly , a mismatch in the theory of the decay of neutral pions ; formal arguments forbid the decay into photons , whereas practical calculations and experiments showed that this was the primary form of decay. The resolution of the problem was completely unknown at

2033-446: A set of equations that imposed duality symmetry, assuming the existence of magnetic monopoles . However, these alternative formulations are less theoretically motivated, and in many cases cannot even be derived from an action . A term analogous to the one that would be added to Maxwell's equations to account for axions also appears in recent (2008) theoretical models for topological insulators giving an effective axion description of

2140-483: A significant role for cosmic strings and currently it is known that the contribution of cosmic strings to the CMB cannot be more than 10%. The violent oscillations of cosmic strings generically lead to the formation of cusps and kinks . These in turn cause parts of the string to pinch off into isolated loops. These loops have a finite lifespan and decay (primarily) via gravitational radiation . This radiation which leads to

2247-403: A six-dimensional bulk. It was once thought that the gravitational influence of cosmic strings might contribute to the large-scale clumping of matter in the universe, but all that is known today through galaxy surveys and precision measurements of the cosmic microwave background (CMB) fits an evolution out of random, gaussian fluctuations. These precise observations therefore tend to rule out

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2354-471: A solution to the apparent transparency of the Universe to TeV photons. It has also been demonstrated that, in the large magnetic fields threading the atmospheres of compact astrophysical objects (e.g., magnetars ), photons will convert much more efficiently. This would in turn give rise to distinct absorption-like features in the spectra detectable by early 21st century telescopes. A new (2009) promising means

2461-435: A theoretical team from Massachusetts Institute of Technology devised a possible way of detecting axions using a strong magnetic field that need be no stronger than that produced in an MRI scanning machine. It would show variation, a slight wavering, that is linked to the mass of the axion. Results from the ensuing experiment published in 2021 reported no evidence of axions in the mass range from 4.1x10 to 8.27x10 eV. In 2022

2568-516: A very small mass in the range from 1 μeV/ c to 1 eV/ c , and very low interaction cross-sections for strong and weak forces. Because of their properties, axions would interact only minimally with ordinary matter. Axions would also change to and from photons in magnetic fields. The properties of the axion, such as the axion mass, decay constant, and abundance, all have implications for cosmology. Inflation theory suggests that if they exist, axions would be created abundantly during

2675-465: A window into string theory. If cosmic strings are observed, which is a real possibility for a wide range of cosmological string models, this would provide the first experimental evidence of a string theory model underlying the structure of spacetime. There are many attempts to detect the footprint of a cosmic strings network. In 1986, John G. Cramer proposed that spacecraft equipped with magnet coils could travel along cosmic strings, analogous to how

2782-407: Is a geometrical structure with an angle deficit, which thus is in tension and hence has positive mass. In 1995, Visser et al. proposed that cosmic strings could theoretically also exist with angle excesses, and thus negative tension and hence negative mass . The stability of such exotic matter strings is problematic; however, they suggested that if a negative mass string were to be wrapped around

2889-416: Is a phenomenon noticed in observations of the "double quasar " called Q0957+561A,B . Originally discovered by Dennis Walsh , Bob Carswell, and Ray Weymann in 1979, the double image of this quasar is caused by a galaxy positioned between it and the Earth. The gravitational lens effect of this intermediate galaxy bends the quasar's light so that it follows two paths of different lengths to Earth. The result

2996-450: Is linearly related to the string tension (= mass per unit length), i.e. the larger the tension, the steeper the cone. Therefore, δ reaches 2π for a certain critical value of the tension, and the cone degenerates to a cylinder. (In visualizing this setup one has to think of a string with a finite thickness.) For even larger, "super-critical" values, δ exceeds 2π and the (two-dimensional) exterior geometry closes up (it becomes compact), ending in

3103-419: Is long-lived and weakly interacting: A perfect dark matter candidate. The oscillations of the axion field about the minimum of the effective potential, the so-called misalignment mechanism, generate a cosmological population of cold axions with an abundance depending on the mass of the axion. With a mass above 5  μeV/ c (10 times the electron mass ) axions could account for dark matter , and thus be both

3210-399: Is looking for quasi-particle refraction in systems with strong magnetic gradients. In particular, the refraction will lead to beam splitting in the radio light curves of highly magnetized pulsars and allow much greater sensitivities than currently achievable. The International Axion Observatory (IAXO) is a proposed fourth generation helioscope . Axions can resonantly convert into photons in

3317-422: Is not predicted by the theory, but must be measured. However, large CP-violating interactions originating from QCD would induce a large electric dipole moment (EDM) for the neutron . Experimental constraints on the unobserved EDM implies CP violation from QCD must be extremely tiny and thus Θ must itself be extremely small. Since Θ could have any value between 0 and 2 π , this presents a "naturalness" problem for

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3424-478: Is now known that string theory contains, in addition to the fundamental strings which define the theory perturbatively, other one-dimensional objects, such as D-strings, and higher-dimensional objects such as D-branes, NS-branes and M-branes partially wrapped on compact internal spacetime dimensions, while being spatially extended in one non-compact dimension. The possibility of large compact dimensions and large warp factors allows strings with tension much lower than

3531-565: Is that we see two images of the same quasar, one arriving a short time after the other (about 417.1 days later). However, a team of astronomers at the Harvard-Smithsonian Center for Astrophysics led by Rudolph Schild studied the quasar and found that during the period between September 1994 and July 1995 the two images appeared to have no time delay; changes in the brightness of the two images occurred simultaneously on four separate occasions. Schild and his team believe that

3638-464: The Big Bang . Because of a unique coupling to the instanton field of the primordial universe (the " misalignment mechanism "), an effective dynamical friction is created during the acquisition of mass, following cosmic inflation . This robs all such primordial axions of their kinetic energy. Ultralight axion (ULA) with m ~ 10 eV/ c is a kind of scalar field dark matter that seems to solve

3745-817: The CERN Axion Solar Telescope converts axions produced in the Sun's core to X-rays, and other experiments search for axions produced in laser light. As of the early 2020s, there are dozens of proposed or ongoing experiments searching for axion dark matter. The equations of axion electrodynamics are typically written in "natural units", where the reduced Planck constant ℏ {\displaystyle \hbar } , speed of light c {\displaystyle c} , and permittivity of free space ε 0 {\displaystyle \varepsilon _{0}} all reduce to 1 when expressed in these "natural units". In this unit system,

3852-577: The Peccei-Quinn mechanism for solving the strong CP problem required such large couplings. However, it was soon realized that "invisible axions" with much smaller couplings also work. Two such classes of models are known in the literature as KSVZ ( Kim – Shifman – Vainshtein – Zakharov ) and DFSZ ( Dine – Fischler – Srednicki – Zhitnitsky ). The very weakly coupled axion is also very light, because axion couplings and mass are proportional. Satisfaction with "invisible axions" changed when it

3959-526: The Primakoff effect , which converts axions to photons and vice versa in electromagnetic fields. The Axion Dark Matter Experiment (ADMX) at the University of Washington uses a strong magnetic field to detect the possible weak conversion of axions to microwaves . ADMX searches the galactic dark matter halo for axions resonant with a cold microwave cavity. ADMX has excluded optimistic axion models in

4066-578: The Slavnov–Taylor identities . The world took little notice, but Veltman was excited because he saw that the problem he had been working on was solved. A period of intense collaboration followed in which they developed the technique of dimensional regularization . Soon 't Hooft's second paper was ready to be published, in which he showed that Yang–Mills theories with massive fields due to spontaneous symmetry breaking could be renormalized. This paper earned them worldwide recognition, and would ultimately earn

4173-785: The XENON1T experiment at the Gran Sasso National Laboratory in Italy reported a result suggesting the discovery of solar axions. The results were not significant at the 5-sigma level required for confirmation, and other explanations of the data were possible though less likely. New observations made in July 2022 after the observatory upgrade to XENONnT discarded the excess, thus ending the possibility of new particle discovery. One theory of axions relevant to cosmology had predicted that they would have no electric charge ,

4280-430: The holographic principle by him and Leonard Susskind . 't Hooft has "deviating views on the physical interpretation of quantum theory ". He believes that there could be a deterministic explanation underlying quantum mechanics. Using a speculative model he has argued that such a theory could avoid the usual Bell inequality arguments that would disallow such a local hidden-variable theory . In 2016 he published

4387-512: The holographic principle . Gerard 't Hooft was born in Den Helder on July 5, 1946, but grew up in The Hague . He was the middle child of a family of three. He comes from a family of scholars. His great uncle was Nobel prize laureate Frits Zernike , and his grandmother was married to Pieter Nicolaas van Kampen , a professor of zoology at Leiden University . His uncle Nico van Kampen

Axion - Misplaced Pages Continue

4494-515: The light-by-light scattering process. Those searches are sensitive for rather large axion masses between 100 MeV/c and hundreds of GeV/c. Assuming a coupling of axions to the Higgs boson, searches for anomalous Higgs boson decays into two axions can theoretically provide even stronger limits. It was reported in 2014 that evidence for axions may have been detected as a seasonal variation in observed X-ray emission that would be expected from conversion in

4601-645: The magnetospheres of neutron stars . The emerging photons lie in the GHz frequency range and can be potentially picked up in radio detectors, leading to a sensitive probe of the axion parameter space. This strategy has been used to constrain the axion–photon coupling in the 5–11 μeV mass range, by re-analyzing existing data from the Green Bank Telescope and the Effelsberg 100 m Radio Telescope . A novel, alternative strategy consists in detecting

4708-530: The post-inflation period on a supercomputer . Progress in the late 2010s in determining the present abundance of a KSVZ-type axion using numerical simulations lead to values between 0.02 and 0.1 meV, although these results have been challenged by the details on the power spectrum of emitted axions from strings. The axion models originally proposed by Wilczek and by Weinberg chose axion coupling strengths that were so strong that they would have already been detected in prior experiments. It had been thought that

4815-527: The 1.9–3.53 μeV range. From 2013 to 2018 a series of upgrades were done and it is taking new data, including at 4.9–6.2 μeV. In December 2021 it excluded the 3.3–4.2 μeV range for the KSVZ model. Other experiments of this type include DMRadio, HAYSTAC, CULTASK, and ORGAN. HAYSTAC completed the first scanning run of a haloscope above 20 μeV in the late 2010s. The Italian PVLAS experiment searches for polarization changes of light propagating in

4922-587: The 1999 Nobel Prize in Physics. For this proof he introduced (with his adviser Veltman) the technique of dimensional regularization. After his PhD, he became interested in the role of gauge theories in the strong interaction, the leading theory of which is called quantum chromodynamics or QCD. Much of his research focused on the problem of color confinement in QCD, i.e. the observational fact that only color neutral particles are observed at low energies. This led him to

5029-511: The Earth's magnetic field of axions streaming from the Sun. Studying 15 years of data by the European Space Agency 's XMM-Newton observatory, a research group at Leicester University noticed a seasonal variation for which no conventional explanation could be found. One potential explanation for the variation, described as "plausible" by the senior author of the paper, is the known seasonal variation in visibility to XMM-Newton of

5136-482: The Netherlands. He shared the 1999 Nobel Prize in Physics with his thesis advisor Martinus J. G. Veltman "for elucidating the quantum structure of electroweak interactions ". His work concentrates on gauge theory , black holes , quantum gravity and fundamental aspects of quantum mechanics. His contributions to physics include a proof that gauge theories are renormalizable , dimensional regularization and

5243-439: The Planck scale. Furthermore, various dualities that have been discovered point to the conclusion that actually all these apparently different types of string are just the same object as it appears in different regions of parameter space. These new developments have largely revived interest in cosmic strings, starting in the early 2000s. In 2002, Henry Tye and collaborators predicted the production of cosmic superstrings during

5350-499: The Universe within which the spontaneous breaking of the PQ symmetry leads to a homogeneous value of the initial value of the axion field. In this "pre-inflationary" scenario, topological defects are inflated away and do not contribute to the axion energy density. However, other bounds that come from isocurvature modes severely constrain this scenario, which require a relatively low-energy scale of inflation to be viable. If at least one of

5457-525: The Wormhole with Morgan Freeman . 't Hooft's research interest can be divided in three main directions: 'gauge theories in elementary particle physics', 'quantum gravity and black holes', and 'foundational aspects of quantum mechanics'. 't Hooft is most famous for his contributions to the development of gauge theories in particle physics. The best known of these is the proof in his PhD thesis that Yang–Mills theories are renormalizable, for which he shared

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5564-434: The axion has both a scalar and a fermionic superpartner . The fermionic superpartner of the axion is called the axino , the scalar superpartner is called the saxion or dilaton . They are all bundled in a chiral superfield . Gerard %27t Hooft Gerardus " Gerard " 't Hooft ( Dutch: [ˈɣeːrɑrt ət ˈɦoːft] ; born July 5, 1946) is a Dutch theoretical physicist and professor at Utrecht University ,

5671-556: The axion itself. Despite not yet having been found, the axion has been well studied for over 40 years, giving time for physicists to develop insight into axion effects that might be detected. Several experimental searches for axions are presently underway; most exploit axions' expected slight interaction with photons in strong magnetic fields. Axions are also one of the few remaining plausible candidates for dark matter particles, and might be discovered in some dark matter experiments. Several experiments search for astrophysical axions by

5778-548: The axion mass to be placed from observations of neutron stars in gamma-rays using the Fermi Gamma-ray Space Telescope . From an analysis of four neutron stars, Berenji et al. (2016) obtained a 95% confidence interval upper limit on the axion mass of 0.079 eV. In 2021 it has been also suggested that a reported excess of hard X-ray emission from a system of neutron stars known as the magnificent seven could be explained as axion emission. In 2016,

5885-403: The conditions (a) or (b) is violated, the axion field takes different values within patches that are initially out of causal contact , but that today populate the volume enclosed by our Hubble horizon . In this scenario, isocurvature fluctuations in the PQ field randomise the axion field, with no preferred value in the power spectrum. The proper treatment in this scenario is to solve numerically

5992-555: The course of his studies he decided he wanted to go into what he perceived as the heart of theoretical physics, elementary particles . His uncle had grown to dislike the subject and in particular its practitioners, so when it became time to write his doctoraalscriptie (former name of the Dutch equivalent of a master's thesis ) in 1968, 't Hooft turned to the newly appointed professor Martinus Veltman , who specialized in Yang–Mills theory ,

6099-442: The critical value by approximately a factor of 1.6), the string cannot be stabilized in radial direction anymore. Realistic cosmic strings are expected to have tensions around 6 orders of magnitude below the critical value, and are thus always sub-critical. However, the inflating cosmic string solutions might be relevant in the context of brane cosmology , where the string is promoted to a 3- brane (corresponding to our universe) in

6206-420: The discovery that SU(N) gauge theories simplify in the large N limit , a fact which has proved important in the examination of the conjectured correspondence between string theories in an Anti-de Sitter space and conformal field theories in one lower dimension. By solving the theory in one space and one time dimension, 't Hooft was able to derive a formula for the masses of mesons . He also studied

6313-507: The electrodynamic equations are: Above, a dot above a variable denotes its time derivative; the dot spaced between variables is the vector dot product ; the factor   g a γ γ   {\displaystyle \ g_{a\gamma \gamma }\ } is the axion-to-photon coupling constant rendered in "natural units". Alternative forms of these equations have been proposed, which imply completely different physical signatures. For example, Visinelli wrote

6420-686: The electrodynamics of these materials. This term leads to several interesting predicted properties including a quantized magnetoelectric effect . Evidence for this effect has been given in THz spectroscopy experiments performed at the Johns Hopkins University on quantum regime thin film topological insulators developed at Rutgers University . In 2019, a team at the Max Planck Institute for Chemical Physics of Solids published their detection of an axion insulator phase of

6527-399: The equation of motion of the PQ field in an expanding Universe, in order to capture all features coming from the misalignment mechanism, including the contribution from topological defects like "axionic" strings and domain walls . An axion mass estimate between 0.05 and 1.50 meV was reported by Borsanyi et al. (2016). The result was calculated by simulating the formation of axions during

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6634-532: The galactic scale. If they continuously fall into galaxies from the intergalactic medium, they would be denser in " caustic " rings, just as the stream of water in a continuously flowing fountain is thicker at its peak. The gravitational effects of these rings on galactic structure and rotation might then be observable. Other cold dark matter theoretical candidates, such as WIMPs and MACHOs , could also form such rings, but because such candidates are fermionic and thus experience friction or scattering among themselves,

6741-458: The ideas of the Dalton Plan , an educational method that suited him well. He excelled at science and mathematics courses. At the age of sixteen he won a silver medal in the second Dutch Math Olympiad . After Gerard 't Hooft passed his high school exams in 1964, he enrolled in the physics program at Utrecht University. He opted for Utrecht instead of the much closer Leiden, because his uncle

6848-492: The implied dark matter density 0.3 ± 0.1 GeV/cm , indicating said axions would not have enough mass to be the sole component of dark matter. The ORGAN experiment plans to conduct a direct test of this result via the haloscope method. Dark matter cryogenic detectors have searched for electron recoils that would indicate axions. CDMS published in 2009 and EDELWEISS set coupling and mass limits in 2013. UORE and XMASS also set limits on solar axions in 2013. XENON100 used

6955-552: The journal from the controversy of ECE theory . 't Hooft held the position until 2016. On July 1, 2011 he was appointed Distinguished professor by Utrecht University. He is married to Albertha Schik (Betteke) and has two daughters. In 1999 't Hooft shared the Nobel prize in Physics with his thesis adviser Veltman for "elucidating the quantum structure of the electroweak interactions in physics". Before that time his work had already been recognized by other notable awards. In 1981, he

7062-428: The last stages of brane inflation , a string theory construction of the early universe that gives leads to an expanding universe and cosmological inflation. It was subsequently realized by string theorist Joseph Polchinski that the expanding Universe could have stretched a "fundamental" string (the sort which superstring theory considers) until it was of intergalactic size. Such a stretched string would exhibit many of

7169-421: The low coupling constant thus predicts that the axion is not scattered out of its state despite its small mass so that the universe would be filled with a very cold Bose–Einstein condensate of primordial axions. Hence, axions could plausibly explain the dark matter problem of physical cosmology . Observational studies are underway, but they are not yet sufficiently sensitive to probe the mass regions if they are

7276-447: The model could be quantized. More recently he proposed generalizing this piecewise flat model of gravity to 4 spacetime dimensions. With Stephen Hawking 's discovery of Hawking radiation of black holes , it appeared that the evaporation of these objects violated a fundamental property of quantum mechanics, unitarity . 't Hooft refused to accept this problem, known as the black hole information paradox , and assumed that this must be

7383-601: The nuclear spin rotation occurs. This precession can be measured using precession magnetometry and if detected, would be evidence for Axions. An experiment using this technique is the Cosmic Axion Spin Precession Experiment (CASPEr). Axions may also be produced at colliders, in particular in electron-positron collisions as well as in ultra-peripheral heavy ion collisions at the Large Hadron Collider at CERN, reinterpreting

7490-426: The only explanation for this observation is that a cosmic string passed between the Earth and the quasar during that time period traveling at very high speed and oscillating with a period of about 100 days. Until 2023 the most sensitive bounds on cosmic string parameters came from the non-detection of gravitational waves by pulsar timing array data. The first detection of gravitational waves with pulsar timing array

7597-523: The other side of the barrier. Experiments by BFRS and a team led by Rizzo ruled out an axion cause. GammeV saw no events, reported in a 2008 Physics Review Letter. ALPS I conducted similar runs, setting new constraints in 2010; ALPS II began collecting data in May 2023. OSQAR found no signal, limiting coupling, and will continue. Axion-like bosons could have a signature in astrophysical settings. In particular, several works have proposed axion-like particles as

7704-632: The pair the 1999 Nobel Prize in Physics. These two papers formed the basis of 't Hooft's dissertation , The Renormalization procedure for Yang–Mills Fields , and he obtained his PhD degree in 1972. In the same year he married his wife, Albertha A. Schik, a student of medicine in Utrecht. After obtaining his doctorate 't Hooft went to CERN in Geneva, where he had a fellowship. He further refined his methods for Yang–Mills theories with Veltman (who went back to Geneva). In this time he became interested in

7811-411: The particle. Because it has a non-zero mass, the axion is a pseudo-Nambu–Goldstone boson . QCD effects produce an effective periodic potential in which the axion field moves. Expanding the potential about one of its minima, one finds that the product of the axion mass with the axion decay constant is determined by the topological susceptibility of the QCD vacuum. An axion with mass much less than 60 keV

7918-556: The photon production, necessary to allow the X-rays to enter the detector that cannot point directly at the sun, would dissipate the flux so much that the probability of detection would be negligible. In 2013, Christian Beck suggested that axions might be detectable in Josephson junctions ; and in 2014, he argued that a signature, consistent with a mass ≈110 μeV, had in fact been observed in several preexisting experiments. In 2020,

8025-552: The polarized light measurements of Messier 87* by the Event Horizon Telescope were used to constrain the mass of the axion assuming that hypothetical clouds of axions could form around a black hole, rejecting the approximate 10 eV/ c – 10 eV/ c range of mass values. Resonance effects may be evident in Josephson junctions from a supposed high flux of axions from the galactic halo with mass of 110 μeV and density 0.05 GeV/cm compared to

8132-504: The possibility of fundamental superstrings having been produced in the early universe and stretched to macroscopic scales, in which case (following the nomenclature of Tom Kibble) they would then be referred to as cosmic superstrings. He concluded that had they been produced they would have either disintegrated into smaller strings before ever reaching macroscopic scales (in the case of Type I superstring theory), they would always appear as boundaries of domain walls whose tension would force

8239-465: The possibility that the strong interaction could be described as a massless Yang–Mills theory, i.e. one of a type that he had just proved to be renormalizable and hence be susceptible to detailed calculation and comparison with experiment. According to 't Hooft's calculations, this type of theory possessed just the right kind of scaling properties ( asymptotic freedom ) that this theory should have according to deep inelastic scattering experiments. This

8346-534: The properties of the old "cosmic" string variety, making the older calculations useful again. As theorist Tom Kibble remarks, "string theory cosmologists have discovered cosmic strings lurking everywhere in the undergrowth". Older proposals for detecting cosmic strings could now be used to investigate superstring theory. Superstrings, D-strings or the other stringy objects mentioned above stretched to intergalactic scales would radiate gravitational waves, which could be detected using experiments like LIGO and especially

8453-520: The renormalization counter terms , which led to the discovery of supergravity . In the 1980s, 't Hooft's attention was drawn to the subject of gravity in 3 spacetime dimensions. Together with Deser and Jackiw he published an article in 1984 describing the dynamics of flat space where the only local degrees of freedom were propagating point defects. His attention returned to this model at various points in time, showing that Gott pairs would not cause causality violating timelike loops , and showing how

8560-414: The result of the semi-classical treatment of Hawking, and that it should not appear in a full theory of quantum gravity. He proposed that it might be possible to study some of the properties of such a theory, by assuming that such a theory was unitary. Using this approach he has argued that near a black hole, quantum fields could be described by a theory in a lower dimension. This led to the introduction of

8667-409: The result was eventually rediscovered and published by Hugh David Politzer , David Gross , and Frank Wilczek in 1973, which led to their earning the 2004 Nobel Prize in Physics . In 1974, 't Hooft returned to Utrecht where he became assistant professor. In 1976, he was invited for a guest position at Stanford and a position at Harvard as Morris Loeb lecturer. His eldest daughter, Saskia Anne,

8774-427: The rings would be less sharply defined. João G. Rosa and Thomas W. Kephart suggested that axion clouds formed around unstable primordial black holes might initiate a chain of reactions that radiate electromagnetic waves, allowing their detection. When adjusting the mass of the axions to explain dark matter, the pair discovered that the value would also explain the luminosity and wavelength of fast radio bursts , being

8881-519: The role of so-called instanton contributions in QCD. His calculation showed that these contributions lead to an interaction between light quarks at low energies not present in the normal theory. Studying instanton solutions of Yang–Mills theories, 't Hooft discovered that spontaneously breaking a theory with SU(N) symmetry to a U(1) symmetry will lead to the existence of magnetic monopoles . These monopoles are called 't Hooft–Polyakov monopoles , after Alexander Polyakov , who independently obtained

8988-561: The same order of magnitude as that of a proton, i.e. ~ 1 fm , or smaller. Given that this scale is much smaller than any cosmological scale, these strings are often studied in the zero-width, or Nambu–Goto approximation. Under this assumption, strings behave as one-dimensional objects and obey the Nambu–Goto action , which is classically equivalent to the Polyakov action that defines the bosonic sector of superstring theory . In field theory,

9095-563: The same result. As another piece in the color confinement puzzle 't Hooft introduced 't Hooft loops , which are the magnetic dual of Wilson loops . Using these operators he was able to classify different phases of QCD, which form the basis of the QCD phase diagram . In 1986, he was finally able to show that instanton contributions solve the Adler–Bell–Jackiw anomaly , the topic of his master's thesis. When Veltman and 't Hooft moved to CERN after 't Hooft obtained his PhD, Veltman's attention

9202-493: The small scale problems of CDM. A single ULA with a GUT scale decay constant provides the correct relic density without fine-tuning. Axions would also have stopped interaction with normal matter at a different moment after the Big Bang than other more massive dark particles. The lingering effects of this difference could perhaps be calculated and observed astronomically. If axions have low mass, thus preventing other decay modes (since there are no lighter particles to decay into),

9309-428: The solution to the dark matter problem with the fuzzy dark matter region starting to be probed via superradiance . High mass axions of the kind searched for by Jain and Singh (2007) would not persist in the modern universe. Moreover, if axions exist, scatterings with other particles in the thermal bath of the early universe unavoidably produce a population of hot axions. Low mass axions could have additional structure at

9416-463: The space-based gravitational wave experiment LISA. They might also cause slight irregularities in the cosmic microwave background, too subtle to have been detected yet but possibly within the realm of future observability. Note that most of these proposals depend, however, on the appropriate cosmological fundamentals (strings, branes, etc.), and no convincing experimental verification of these has been confirmed to date. Cosmic strings nevertheless provide

9523-464: The standard model. Why should this parameter find itself so close to zero? (Or, why should QCD find itself CP-preserving?) This question constitutes what is known as the strong CP problem . In 1977, Roberto Peccei and Helen Quinn postulated a more elegant solution to the strong CP problem, the Peccei–Quinn mechanism . The idea is to effectively promote Θ to a field. This is accomplished by adding

9630-561: The strength of interactions and the curvature of spacetime.) A string is a geometrical deviation from Euclidean geometry in spacetime characterized by an angular deficit: a circle around the outside of a string would comprise a total angle less than 360°. From the general theory of relativity such a geometrical defect must be in tension, and would be manifested by mass. Even though cosmic strings are thought to be extremely thin, they would have immense density, and so would represent significant gravitational wave sources. A cosmic string about

9737-409: The string width is set by the scale of the symmetry breaking phase transition. In string theory, the string width is set (in the simplest cases) by the fundamental string scale, warp factors (associated to the spacetime curvature of an internal six-dimensional spacetime manifold) and/or the size of internal compact dimensions . (In string theory, the universe is either 10- or 11-dimensional, depending on

9844-469: The strings to collapse rather than grow to cosmic scales (in the context of heterotic superstring theory), or having a characteristic energy scale close to the Planck energy they would be produced before cosmological inflation and hence be diluted away with the expansion of the universe and not be observable. Much has changed since these early days, primarily due to the second superstring revolution . It

9951-412: The strongest signal from cosmic strings may in turn be detectable in gravitational wave observatories . An important open question is to what extent do the pinched off loops backreact or change the initial state of the emitting cosmic string—such backreaction effects are almost always neglected in computations and are known to be important, even for order of magnitude estimates. Gravitational lensing of

10058-477: The sunward magnetosphere in which X-rays may be produced by axions from the Sun's core. This interpretation of the seasonal variation is disputed by two Italian researchers, who identify flaws in the arguments of the Leicester group that are said to rule out an interpretation in terms of axions. Most importantly, the scattering in angle assumed by the Leicester group to be caused by magnetic field gradients during

10165-487: The time, and 't Hooft was unable to provide one. In 1969, 't Hooft started on his doctoral research with Martinus Veltman as his advisor. He would work on the same subject Veltman was working on, the renormalization of Yang–Mills theories. In 1971 his first paper was published. In it he showed how to renormalize massless Yang–Mills fields, and was able to derive relations between amplitudes, which would be generalized by Andrei Slavnov and John C. Taylor , and become known as

10272-503: The transient signal from the encounter between a neutron star and an axion minicluster in the Milky Way . Axions can be produced in the Sun's core when X-rays scatter in strong electric fields. The CAST solar telescope is underway, and has set limits on coupling to photons and electrons. Axions may also be produced within neutron stars by nucleon–nucleon bremsstrahlung . The subsequent decay of axions to gamma rays allows constraints on

10379-543: Was a professor there and he wanted to attend his lectures. Because he was so focused on science, his father insisted that he join the Utrechtsch Studenten Corps, a student association, in the hope that he would do something else besides studying. This worked to some extent; during his studies he was a coxswain with their rowing club "Triton" and organized a national congress for science students with their science discussion club "Christiaan Huygens". In

10486-808: Was also honoured with a Franklin Medal . In 2000, 't Hooft received the Golden Plate Award of the American Academy of Achievement . Since his Nobel Prize, 't Hooft has received a slew of awards, honorary doctorates and honorary professorships. He was knighted commander in the Order of the Netherlands Lion , and officer in the French Legion of Honor . The asteroid 9491 Thooft has been named in his honor, and he has written

10593-465: Was an (emeritus) professor of theoretical physics at Utrecht University, and his mother married a maritime engineer. Following his family's footsteps, he showed interest in science at an early age. When his primary school teacher asked him what he wanted to be when he grew up, he replied, "a man who knows everything." After primary school Gerard attended the Dalton Lyceum, a school that applied

10700-584: Was awarded the Wolf Prize , possibly the most prestigious prize in physics after the Nobel prize. Five years later he received the Lorentz Medal , awarded every four years in recognition of the most important contributions in theoretical physics. In 1995, he was one of the first recipients of the Spinozapremie , the highest award available to scientists in the Netherlands. In the same year he

10807-607: Was born in Boston , while his second daughter, Ellen Marga, was born in 1978 after he returned to Utrecht, where he was made full professor. In the academic year 1987–1988 't Hooft spent a sabbatical in the Boston University Physics Department along with Howard Georgi , Robert Jaffe and others arranged by the then new Department chair Lawrence Sulak . In 2007 't Hooft became editor-in-chief for Foundations of Physics , where he sought to distance

10914-491: Was confirmed in 2023. The earthbound Laser Interferometer Gravitational-Wave Observatory (LIGO) and especially the space-based gravitational wave detector Laser Interferometer Space Antenna (LISA) will search for gravitational waves and are likely to be sensitive enough to detect signals from cosmic strings, provided the relevant cosmic string tensions are not too small. During the early days of string theory both string theorists and cosmic string theorists believed that there

11021-512: Was contrary to popular perception of Yang–Mills theories at the time, that like gravitation and electrodynamics, their intensity should decrease with increasing distance between the interacting particles; such conventional behaviour with distance was unable to explain the results of deep inelastic scattering, whereas 't Hooft's calculations could. When 't Hooft mentioned his results at a small conference at Marseilles in 1972, Kurt Symanzik urged him to publish this result; but 't Hooft did not, and

11128-467: Was drawn to the possibility of using their dimensional regularization techniques to the problem of quantizing gravity. Although it was known that perturbative quantum gravity was not completely renormalizible, they felt important lessons were to be learned by studying the formal renormalization of the theory order by order. This work would be continued by Stanley Deser and another PhD student of Veltman, Peter van Nieuwenhuizen , who later found patterns in

11235-462: Was first contemplated by the theoretical physicist Tom Kibble in the 1970s. The formation of cosmic strings is somewhat analogous to the imperfections that form between crystal grains in solidifying liquids, or the cracks that form when water freezes into ice. The phase transitions leading to the production of cosmic strings are likely to have occurred during the earliest moments of the universe's evolution, just after cosmological inflation , and are

11342-428: Was no direct connection between superstrings and cosmic strings (the names were chosen independently by analogy with ordinary string ). The possibility of cosmic strings being produced in the early universe was first envisioned by quantum field theorist Tom Kibble in 1976, and this sprouted the first flurry of interest in the field. In 1985, during the first superstring revolution , Edward Witten contemplated on

11449-554: Was shown that any very light axion would have been overproduced in the early universe and therefore must be excluded. Pierre Sikivie computed how Maxwell's equations are modified in the presence of an axion in 1983. He showed that these axions could be detected on Earth by converting them to photons, using a strong magnetic field, motivating a number of experiments. For example, the Axion Dark Matter Experiment converts axion dark matter to microwave photons,

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