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57-702: D-branes were discovered by Jin Dai, Leigh , and Polchinski , and independently by Hořava , in 1989. In 1995, Polchinski identified D-branes with black p-brane solutions of supergravity , a discovery that triggered the Second Superstring Revolution and led to both holographic and M-theory dualities. The equations of motion of string theory require that the endpoints of an open string (a string with endpoints) satisfy one of two types of boundary conditions: The Neumann boundary condition , corresponding to free endpoints moving through spacetime at

114-439: A U (1) gauge theory where the gauge group is made of unitary matrices of order 1. D-branes can be used to generate gauge theories of higher order, in the following way: Consider a group of N separate D p -branes, arranged in parallel for simplicity. The branes are labeled 1,2,..., N for convenience. Open strings in this system exist in one of many sectors: the strings beginning and ending on some brane i give that brane

171-457: A p -dimensional hyperplane. This hyperplane provides one description of a D p -brane. Although rigid in the limit of zero coupling, the spectrum of open strings ending on a D-brane contains modes associated with its fluctuations, implying that D-branes are dynamical objects. When N {\displaystyle N} D-branes are nearly coincident, the spectrum of strings stretching between them becomes very rich. One set of modes produce

228-455: A thought experiment , dropping an amount of hot gas into a black hole. Since the gas cannot escape from the hole's gravitational pull, its entropy would seem to have vanished from the universe. In order to maintain the second law of thermodynamics , one must postulate that the black hole gained whatever entropy the infalling gas originally had. Attempting to apply quantum mechanics to the study of black holes, Stephen Hawking discovered that

285-489: A Maxwell field and some massless scalar fields on its volume. The strings stretching from brane i to another brane j have more intriguing properties. For starters, it is worthwhile to ask which sectors of strings can interact with one another. One straightforward mechanism for a string interaction is for two strings to join endpoints (or, conversely, for one string to "split down the middle" and make two "daughter" strings). Since endpoints are restricted to lie on D-branes, it

342-459: A comparable upper bound of 3.16 × 10  eV/ c . The gravitational wave and planetary ephemeris need not agree: they test different aspects of a potential graviton-based theory. Astronomical observations of the kinematics of galaxies, especially the galaxy rotation problem and modified Newtonian dynamics , might point toward gravitons having non-zero mass. Most theories containing gravitons suffer from severe problems. Attempts to extend

399-456: A constant velocity can be mapped to the problem of two stationary branes that are rotated relative to each other by some angle. The annulus amplitude yields singularities that correspond to the on-shell production of open strings stretched between the two branes. This is true irrespective of the charge of the D-branes. At non-relativistic scattering velocities the open strings may be described by

456-456: A different area of physics, and have become quite useful in their own right. If nothing else, the relation between D-brane geometry and gauge theory offers a useful pedagogical tool for explaining gauge interactions, even if string theory fails to be the "theory of everything". Another important use of D-branes has been in the study of black holes . Since the 1970s, scientists have debated the problem of black holes having entropy . Consider, as

513-484: A first-order tensor). Additionally, it can be shown that any massless spin-2 field would give rise to a force indistinguishable from gravitation, because a massless spin-2 field would couple to the stress–energy tensor in the same way gravitational interactions do. This result suggests that, if a massless spin-2 particle is discovered, it must be the graviton. It is hypothesized that gravitational interactions are mediated by an as yet undiscovered elementary particle, dubbed

570-407: A fundamental string. If it exists, the graviton is expected to be massless because the gravitational force has a very long range, and appears to propagate at the speed of light. The graviton must be a spin -2 boson because the source of gravitation is the stress–energy tensor , a second-order tensor (compared with electromagnetism 's spin-1 photon , the source of which is the four-current ,

627-574: A hole should emit energy with the characteristic spectrum of thermal radiation. The characteristic temperature of this Hawking radiation is given by T H = ℏ c 3 8 π G M k B ( ≈ 1.227 × 10 23 k g M K ) , {\displaystyle T_{\rm {H}}={\frac {\hbar c^{3}}{8\pi GMk_{\text{B}}}}\;\quad (\approx {1.227\times 10^{23}\;kg \over M}\;K),} where G {\displaystyle G}

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684-453: A low-energy effective action that contains two complex scalar fields that are coupled via a term ϕ 2 χ 2 {\displaystyle \phi ^{2}\chi ^{2}} . Thus, as the field ϕ {\displaystyle \phi } (separation of the branes) changes, the mass of the field χ {\displaystyle \chi } changes. This induces open string production and as

741-405: A necessary part of the theory if we permit open strings to exist, and all D-branes carry an electromagnetic field on their volume. Other particle states originate from strings beginning and ending on the same D-brane. Some correspond to massless particles like the photon; also in this group are a set of massless scalar particles. If a D p -brane is embedded in a spacetime of d spatial dimensions,

798-485: A non-abelian gauge theory on the world-volume. Another set of modes is an N × N {\displaystyle N\times N} dimensional matrix for each transverse dimension of the brane. If these matrices commute, they may be diagonalized, and the eigenvalues define the position of the N {\displaystyle N} D-branes in space. More generally, the branes are described by non-commutative geometry, which allows exotic behavior such as

855-510: A reason why the extra dimensions are not apparent. One possibility would be that the visible Universe is in fact a very large D-brane extending over three spatial dimensions. Material objects, made of open strings, are bound to the D-brane, and cannot move "at right angles to reality" to explore the Universe outside the brane. This scenario is called a brane cosmology . The force of gravity

912-637: A result the two scattering branes will be trapped. The arrangement of D-branes constricts the types of string states which can exist in a system. For example, if we have two parallel D2-branes, we can easily imagine strings stretching from brane 1 to brane 2 or vice versa. (In most theories, strings are oriented objects: each one carries an "arrow" defining a direction along its length.) The open strings permissible in this situation then fall into two categories, or "sectors": those originating on brane 1 and terminating on brane 2, and those originating on brane 2 and terminating on brane 1. Symbolically, we say we have

969-449: A string's endpoint to a brane influences the way the string can move and vibrate. Because particle states "emerge" from the string theory as the different vibrational states the string can experience, the arrangement of D-branes controls the types of particles present in the theory. The simplest case is the [1 1] sector for a D p -brane, that is to say the strings which begin and end on any particular D-brane of p dimensions. Examining

1026-471: Is not due to open strings; the gravitons which carry gravitational forces are vibrational states of closed strings. Because closed strings do not have to be attached to D-branes, gravitational effects could depend upon the extra dimensions orthogonal to the brane. When two D-branes approach each other the interaction is captured by the one loop annulus amplitude of strings between the two branes. The scenario of two parallel branes approaching each other at

1083-467: Is a Canadian physicist working on string theory . Leigh obtained his B.Sc. degree from the University of Guelph in 1986, and his Ph.D. from the University of Texas at Austin in 1991, working with Joe Polchinski . After postdoctoral positions at Santa Cruz and Rutgers , he has been a professor at the University of Illinois at Urbana-Champaign since 1996. Since 2007, he has been a Fellow of

1140-426: Is analogous to the ideal gas studied in introductory thermodynamics: the easiest situation to model is when the gas atoms do not have interactions among themselves. Developing the kinetic theory of gases in the case where the gas atoms or molecules experience inter-particle forces (like the van der Waals force ) is more difficult. However, a world without interactions is an uninteresting place: most significantly for

1197-429: Is evident that a [1 2] string may interact with a [2 3] string, but not with a [3 4] or a [4 17] one. The masses of these strings will be influenced by the separation between the branes, as discussed above, so for simplicity's sake, we can imagine the branes squeezed closer and closer together until they lie atop one another. If we regard two overlapping branes as distinct objects, then we still have all

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1254-580: Is proportional to the black hole mass squared; because the Schwarzschild radius is proportional to the mass, the Bekenstein entropy is proportional to the black hole's surface area. In fact, S B = A k B 4 l P 2 , {\displaystyle S_{\rm {B}}={\frac {Ak_{B}}{4l_{\rm {P}}^{2}}},} where l P {\displaystyle l_{\rm {P}}}

1311-814: Is the Newtonian constant of gravitation , M {\displaystyle M} is the black hole's mass and k B {\displaystyle k_{\text{B}}} is the Boltzmann constant . Using this expression for the Hawking temperature, and assuming that a zero-mass black hole has zero entropy, one can use thermodynamic arguments to derive the " Bekenstein entropy": S B = k B 4 π G ℏ c M 2 . {\displaystyle S_{\rm {B}}={\frac {k_{\text{B}}4\pi G}{\hbar c}}M^{2}.} The Bekenstein entropy

1368-600: Is the Planck length . The concept of black hole entropy poses some interesting conundra. In an ordinary situation, a system has entropy when a large number of different "microstates" can satisfy the same macroscopic condition. For example, given a box full of gas, many different arrangements of the gas atoms can have the same total energy. However, a black hole was believed to be a featureless object (in John Wheeler 's catchphrase, " Black holes have no hair "). What, then, are

1425-400: Is the extremely low cross section for the interaction of gravitons with matter. For example, a detector with the mass of Jupiter and 100% efficiency, placed in close orbit around a neutron star , would only be expected to observe one graviton every 10 years, even under the most favorable conditions. It would be impossible to discriminate these events from the background of neutrinos , since

1482-549: The American Physical Society . Leigh discovered, in association with Dai and Polchinski , an important class of extended objects in string theory , the D-branes . This article about a Canadian scientist is a stub . You can help Misplaced Pages by expanding it . This article about a physicist is a stub . You can help Misplaced Pages by expanding it . Graviton In theories of quantum gravity ,

1539-488: The K-theory of the spacetime . Tachyon condensation is still very poorly understood. This is due to the lack of an exact string field theory that would describe the off-shell evolution of the tachyon. This has implications for physical cosmology . Because string theory implies that the Universe has more dimensions than we expect—26 for bosonic string theories and 10 for superstring theories —we have to find

1596-549: The Myers effect , in which a collection of D p -branes expand into a D( p +2)-brane. Tachyon condensation is a central concept in this field. Ashoke Sen has argued that in Type IIB string theory , tachyon condensation allows (in the absence of Neveu-Schwarz 3- form flux) an arbitrary D-brane configuration to be obtained from a stack of D9 and anti D9-branes. Edward Witten has shown that such configurations will be classified by

1653-503: The classical theory of Feynman diagrams and semiclassical corrections such as one-loop diagrams behave normally. However, Feynman diagrams with at least two loops lead to ultraviolet divergences . These infinite results cannot be removed because quantized general relativity is not perturbatively renormalizable , unlike quantum electrodynamics and models such as the Yang–Mills theory . Therefore, incalculable answers are found from

1710-406: The graviton is the hypothetical quantum of gravity , an elementary particle that mediates the force of gravitational interaction. There is no complete quantum field theory of gravitons due to an outstanding mathematical problem with renormalization in general relativity . In string theory , believed by some to be a consistent theory of quantum gravity, the graviton is a massless state of

1767-542: The graviton . The three other known forces of nature are mediated by elementary particles: electromagnetism by the photon , the strong interaction by gluons , and the weak interaction by the W and Z bosons . All three of these forces appear to be accurately described by the Standard Model of particle physics. In the classical limit , a successful theory of gravitons would reduce to general relativity , which itself reduces to Newton's law of gravitation in

D-brane - Misplaced Pages Continue

1824-574: The moduli space of any open string theory. The Dai et al. paper also notes that the locus of the Dirichlet boundary conditions is dynamical, and coins the term Dirichlet-brane (D-brane) for the resulting object (this paper also coins orientifold for another object that arises under string T-duality). A 1989 paper by Leigh showed that D-brane dynamics are governed by the Dirac–Born–Infeld action . D-instantons were extensively studied by Green in

1881-456: The strong interaction . String compactifications studied by Harvey and Minahan, Ishibashi and Onogi, and Pradisi and Sagnotti in 1987–1989 also employed Dirichlet boundary conditions. In 1989, Dai, Leigh , Polchinski , and Hořava independently, discovered that T-duality interchanges the usual Neumann boundary conditions with Dirichlet boundary conditions. This result implies that such boundary conditions must necessarily appear in regions of

1938-487: The "degrees of freedom" which can give rise to black hole entropy? String theorists have constructed models in which a black hole is a very long (and hence very massive) string. This model gives rough agreement with the expected entropy of a Schwarzschild black hole, but an exact proof has yet to be found one way or the other. The chief difficulty is that it is relatively easy to count the degrees of freedom quantum strings possess if they do not interact with one another. This

1995-504: The "true" space-time background, general relativity is said to be background-independent . In contrast, the Standard Model is not background-independent, with Minkowski space enjoying a special status as the fixed background space-time. A theory of quantum gravity is needed in order to reconcile these differences. Whether this theory should be background-independent is an open question. The answer to this question will determine

2052-495: The Dirichlet conditions were dynamical rather than static. Mixed Dirichlet/Neumann boundary conditions were first considered by Warren Siegel in 1976 as a means of lowering the critical dimension of open string theory from 26 or 10 to 4 (Siegel also cites unpublished work by Halpern, and a 1974 paper by Chodos and Thorn, but a reading of the latter paper shows that it is actually concerned with linear dilation backgrounds, not Dirichlet boundary conditions). This paper, though prescient,

2109-424: The Standard Model or other quantum field theories by adding gravitons run into serious theoretical difficulties at energies close to or above the Planck scale . This is because of infinities arising due to quantum effects; technically, gravitation is not renormalizable . Since classical general relativity and quantum mechanics seem to be incompatible at such energies, from a theoretical point of view, this situation

2166-399: The [1 2] and the [2 1] sectors. In addition, a string may begin and end on the same brane, giving [1 1] and [2 2] sectors. (The numbers inside the brackets are called Chan–Paton indices , but they are really just labels identifying the branes.) A string in either the [1 2] or the [2 1] sector has a minimum length: it cannot be shorter than the separation between

2223-684: The analysis of gravitational waves yielded a new upper bound on the mass of gravitons. The graviton's Compton wavelength is at least 1.6 × 10   m , or about 1.6 light-years , corresponding to a graviton mass of no more than 7.7 × 10   eV / c . This relation between wavelength and mass-energy is calculated with the Planck–Einstein relation , the same formula that relates electromagnetic wavelength to photon energy . Unambiguous detection of individual gravitons, though not prohibited by any fundamental law, has been thought to be impossible with any physically reasonable detector. The reason

2280-452: The black hole problem, gravity is an interaction, and so if the "string coupling" is turned off, no black hole could ever arise. Therefore, calculating black hole entropy requires working in a regime where string interactions exist. Extending the simpler case of non-interacting strings to the regime where a black hole could exist requires supersymmetry . In certain cases, the entropy calculation done for zero string coupling remains valid when

2337-461: The brane carries (in addition to its Maxwell field) a set of d − p massless scalars (particles which do not have polarizations like the photons making up light). Intriguingly, there are just as many massless scalars as there are directions perpendicular to the brane; the geometry of the brane arrangement is closely related to the quantum field theory of the particles existing on it. In fact, these massless scalars are Goldstone excitations of

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2394-406: The brane, corresponding to the different ways the symmetry of empty space can be broken. Placing a D-brane in a universe breaks the symmetry among locations, because it defines a particular place, assigning a special meaning to a particular location along each of the d − p directions perpendicular to the brane. The quantum version of Maxwell's electromagnetism is only one kind of gauge theory ,

2451-413: The branes. All strings have some tension, against which one must pull to lengthen the object; this pull does work on the string, adding to its energy. Because string theories are by nature relativistic , adding energy to a string is equivalent to adding mass, by Einstein's relation E = mc . Therefore, the separation between D-branes controls the minimum mass open strings may have. Furthermore, affixing

2508-574: The consequences of the Nambu–Goto action (and applying the rules of quantum mechanics to quantize the string), one finds that among the spectrum of particles is one resembling the photon , the fundamental quantum of the electromagnetic field. The resemblance is precise: a p -dimensional version of the electromagnetic field, obeying a p -dimensional analogue of Maxwell's equations , exists on every D p -brane. In this sense, then, one can say that string theory "predicts" electromagnetism: D-branes are

2565-608: The dimensions of the required neutrino shield would ensure collapse into a black hole . It has been proposed that detecting single gravitons would be possible by quantum sensing. Even quantum events may not indicate quantization of gravitational radiation. LIGO and Virgo collaborations' observations have directly detected gravitational waves. Others have postulated that graviton scattering yields gravitational waves as particle interactions yield coherent states . Although these experiments cannot detect individual gravitons, they might provide information about certain properties of

2622-415: The early 1990s, and were shown by Polchinski in 1994 to produce the e nonperturbative string effects anticipated by Shenker . In 1995 Polchinski showed that D-branes are the sources of electric and magnetic Ramond–Ramond fields that are required by string duality , leading to rapid progress in the nonperturbative understanding of string theory. Robert Leigh (physicist) Robert Graham Leigh

2679-512: The familiar case, the Schwarzschild black holes observed in our own universe. Dirichlet boundary conditions and D-branes had a long "pre-history" before their full significance was recognized. A series of 1975–76 papers by Bardeen, Bars, Hanson and Peccei dealt with an early concrete proposal of interacting particles at the ends of strings (quarks interacting with QCD flux tubes), with dynamical boundary conditions for string endpoints where

2736-496: The gravitational interaction by particles was anticipated by Pierre-Simon Laplace . Just like Newton's anticipation of photons , Laplace's anticipated "gravitons" had a greater speed than the speed of light in vacuum c {\displaystyle c} , the speed of gravitons expected in modern theories, and were not connected to quantum mechanics or special relativity , since these theories didn't yet exist during Laplace's lifetime. When describing graviton interactions,

2793-453: The graviton plays a role in general relativity , in defining the spacetime in which events take place. In some descriptions energy modifies the "shape" of spacetime itself, and gravity is a result of this shape, an idea which at first glance may appear hard to match with the idea of a force acting between particles. Because the diffeomorphism invariance of the theory does not allow any particular space-time background to be singled out as

2850-516: The graviton. For example, if gravitational waves were observed to propagate slower than c (the speed of light in vacuum), that would imply that the graviton has mass (however, gravitational waves must propagate slower than c in a region with non-zero mass density if they are to be detectable). Observations of gravitational waves put an upper bound of 1.76 × 10  eV/ c on the graviton's mass. Solar system planetary trajectory measurements by space missions such as Cassini and MESSENGER give

2907-451: The perturbation method by which physicists calculate the probability of a particle to emit or absorb gravitons, and the theory loses predictive veracity. Those problems and the complementary approximation framework are grounds to show that a theory more unified than quantized general relativity is required to describe the behavior near the Planck scale . Like the force carriers of the other forces (see photon , gluon , W and Z bosons ),

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2964-469: The sectors we had before, but without the effects due to the brane separations. The zero-mass states in the open-string particle spectrum for a system of N coincident D-branes yields a set of interacting quantum fields which is exactly a U ( N ) gauge theory. (The string theory does contain other interactions, but they are only detectable at very high energies.) Gauge theories were not invented starting with bosonic or fermionic strings; they originated from

3021-533: The speed of light, or the Dirichlet boundary conditions , which pin the string endpoint. Each coordinate of the string must satisfy one or the other of these conditions. There can also exist strings with mixed boundary conditions, where the two endpoints satisfy NN, DD, ND and DN boundary conditions. If p spatial dimensions satisfy the Neumann boundary condition, then the string endpoint is confined to move within

3078-507: The strings interact. The challenge for a string theorist is to devise a situation in which a black hole can exist which does not "break" supersymmetry. In recent years, this has been done by building black holes out of D-branes. Calculating the entropies of these hypothetical holes gives results which agree with the expected Bekenstein entropy. Unfortunately, the cases studied so far all involve higher-dimensional spaces – D5-branes in nine-dimensional space, for example. They do not directly apply to

3135-446: The understanding of what specific role gravitation plays in the fate of the universe. While gravitons are presumed to be massless , they would still carry energy , as does any other quantum particle. Photon energy and gluon energy are also carried by massless particles. It is unclear which variables might determine graviton energy, the amount of energy carried by a single graviton. Alternatively, if gravitons are massive at all ,

3192-445: The weak-field limit. Albert Einstein discussed quantized gravitational radiation in 1916, the year following his publication of general relativity . The term graviton was coined in 1934 by Soviet physicists Dmitry Blokhintsev and Fyodor Galperin  [ ru ] . Paul Dirac reintroduced the term in a number of lectures in 1959, noting that the energy of the gravitational field should come in quanta. A mediation of

3249-400: Was little-noted in its time (a 1985 parody by Siegel, "The Super-g String", contains an almost dead-on description of braneworlds). Dirichlet conditions for all coordinates including Euclidean time (defining what are now known as D-instantons) were introduced by Michael Green in 1977 as a means of introducing point-like structure into string theory, in an attempt to construct a string theory of

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