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98-480: In theoretical physics , the anti-de Sitter/conformal field theory correspondence (frequently abbreviated as AdS/CFT) is a conjectured relationship between two kinds of physical theories. On one side are anti-de Sitter spaces (AdS) that are used in theories of quantum gravity , formulated in terms of string theory or M-theory . On the other side of the correspondence are conformal field theories (CFT) that are quantum field theories , including theories similar to

196-465: A definition of string theory in the special case where the gravitational field is asymptotically anti-de Sitter (that is, when the gravitational field resembles that of anti-de Sitter space at spatial infinity). Physically interesting quantities in string theory are defined in terms of quantities in the dual quantum field theory. In 1975, Stephen Hawking published a calculation that suggested that black holes are not completely black but emit

294-549: A luminiferous aether . Conversely, Einstein was awarded the Nobel Prize for explaining the photoelectric effect , previously an experimental result lacking a theoretical formulation. A physical theory is a model of physical events. It is judged by the extent to which its predictions agree with empirical observations. The quality of a physical theory is also judged on its ability to make new predictions which can be verified by new observations. A physical theory differs from

392-429: A massless spin-2 particle whereas no such particle appears in the physics of hadrons. Such a particle would mediate a force with the properties of gravity. In 1974, Joël Scherk and John Schwarz suggested that string theory was therefore not a theory of nuclear physics as many theorists had thought but instead a theory of quantum gravity. At the same time, it was realized that hadrons are actually made of quarks, and

490-504: A mathematical theorem in that while both are based on some form of axioms , judgment of mathematical applicability is not based on agreement with any experimental results. A physical theory similarly differs from a mathematical theory , in the sense that the word "theory" has a different meaning in mathematical terms. R i c = k g {\displaystyle \mathrm {Ric} =kg} The equations for an Einstein manifold , used in general relativity to describe

588-482: A working hypothesis . Compactification (physics) In theoretical physics , compactification means changing a theory with respect to one of its space-time dimensions . Instead of having a theory with this dimension being infinite, one changes the theory so that this dimension has a finite length, and may also be periodic . Compactification plays an important part in thermal field theory where one compactifies time, in string theory where one compactifies

686-411: A 40 percent chance of colliding. Notice that the boundary of anti-de Sitter space has fewer dimensions than anti-de Sitter space itself. For instance, in the three-dimensional example illustrated above, the boundary is a two-dimensional surface. The AdS/CFT correspondence is often described as a "holographic duality" because this relationship between the two theories is similar to the relationship between

784-404: A certain economy and elegance (compare to mathematical beauty ), a notion sometimes called " Occam's razor " after the 13th-century English philosopher William of Occam (or Ockham), in which the simpler of two theories that describe the same matter just as adequately is preferred (but conceptual simplicity may mean mathematical complexity). They are also more likely to be accepted if they connect

882-524: A concrete mechanism by which they might preserve information. On January 1, 1998, Juan Maldacena published a landmark paper that initiated the study of AdS/CFT. According to Alexander Markovich Polyakov , "[Maldacena's] work opened the flood gates." The conjecture immediately excited great interest in the string theory community and was considered in a paper by Steven Gubser , Igor Klebanov and Polyakov, and another paper of Edward Witten . These papers made Maldacena's conjecture more precise and showed that

980-410: A counterpart in the other theory. For example, a single particle in the gravitational theory might correspond to some collection of particles in the boundary theory. In addition, the predictions in the two theories are quantitatively identical so that if two particles have a 40 percent chance of colliding in the gravitational theory, then the corresponding collections in the boundary theory would also have

1078-458: A dim radiation due to quantum effects near the event horizon . At first, Hawking's result posed a problem for theorists because it suggested that black holes destroy information. More precisely, Hawking's calculation seemed to conflict with one of the basic postulates of quantum mechanics , which states that physical systems evolve in time according to the Schrödinger equation . This property

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1176-500: A form of protoscience and others are a form of pseudoscience . The falsification of the original theory sometimes leads to reformulation of the theory. "Thought" experiments are situations created in one's mind, asking a question akin to "suppose you are in this situation, assuming such is true, what would follow?". They are usually created to investigate phenomena that are not readily experienced in every-day situations. Famous examples of such thought experiments are Schrödinger's cat ,

1274-498: A new branch of mathematics: infinite, orthogonal series . Modern theoretical physics attempts to unify theories and explain phenomena in further attempts to understand the Universe , from the cosmological to the elementary particle scale. Where experimentation cannot be done, theoretical physics still tries to advance through the use of mathematical models. Mainstream theories (sometimes referred to as central theories ) are

1372-465: A physical system might be modeled; e.g., the notion, due to Riemann and others, that space itself might be curved. Theoretical problems that need computational investigation are often the concern of computational physics . Theoretical advances may consist in setting aside old, incorrect paradigms (e.g., aether theory of light propagation, caloric theory of heat, burning consisting of evolving phlogiston , or astronomical bodies revolving around

1470-561: A powerful toolkit for studying strongly coupled quantum field theories. Much of the usefulness of the duality results from the fact that it is a strong–weak duality: when the fields of the quantum field theory are strongly interacting, the ones in the gravitational theory are weakly interacting and thus more mathematically tractable. This fact has been used to study many aspects of nuclear and condensed matter physics by translating problems in those subjects into more mathematically tractable problems in string theory. The AdS/CFT correspondence

1568-426: A procedure known as T-duality . The formulation of more precise versions of the meaning of compactification in this context has been promoted by discoveries such as the mysterious duality. A flux compactification is a particular way to deal with additional dimensions required by string theory. It assumes that the shape of the internal manifold is a Calabi–Yau manifold or generalized Calabi–Yau manifold which

1666-409: A process known as compactification . This produces a theory in which spacetime has effectively a lower number of dimensions and the extra dimensions are "curled up" into circles. A standard analogy for compactification is to consider a multidimensional object such as a garden hose. If the hose is viewed from a sufficient distance, it appears to have only one dimension, its length, but as one approaches

1764-475: A quantum critical point, both time and space may be scaling, but even there we still have a preferred coordinate system and, usually, a lattice. There is some evidence of other linear-T phases to the left of the strange metal about which they are welcome to speculate, but again in this case the condensed-matter problem is overdetermined by experimental facts. The discovery of the AdS/CFT correspondence in late 1997

1862-415: A string. In the late 1960s, experimentalists had found that hadrons fall into families called Regge trajectories with squared energy proportional to angular momentum , and theorists showed that this relationship emerges naturally from the physics of a rotating relativistic string. On the other hand, attempts to model hadrons as strings faced serious problems. One problem was that string theory includes

1960-467: A superfluid, but as experimentalists increase the intensity of the lasers, they become less mobile and then suddenly transition to an insulating state. During the transition, the atoms behave in an unusual way. For example, the atoms slow to a halt at a rate that depends on the temperature and on the Planck constant, the fundamental parameter of quantum mechanics, which does not enter into the description of

2058-422: A three-dimensional object and its image as a hologram . Although a hologram is two-dimensional, it encodes information about all three dimensions of the object it represents. In the same way, theories that are related by the AdS/CFT correspondence are conjectured to be exactly equivalent, despite living in different numbers of dimensions. The conformal field theory is like a hologram that captures information about

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2156-478: A variety of reasons, both physical and mathematical. Yet another realization of the correspondence states that M-theory on AdS 4 × S is equivalent to the ABJM superconformal field theory in three dimensions. Here the gravitational theory has four noncompact dimensions, so this version of the correspondence provides a somewhat more realistic description of gravity. In quantum field theory, one typically computes

2254-403: A way that all the triangles and squares are the same size and the circular outer boundary is infinitely far from any point in the interior. Now imagine a stack of hyperbolic disks where each disk represents the state of the universe at a given time. The resulting geometric object is three-dimensional anti-de Sitter space. It looks like a solid cylinder in which any cross section is a copy of

2352-469: A wide range of phenomena. Testing the consequences of a theory is part of the scientific method . Physical theories can be grouped into three categories: mainstream theories , proposed theories and fringe theories . Theoretical physics began at least 2,300 years ago, under the Pre-socratic philosophy , and continued by Plato and Aristotle , whose views held sway for a millennium. During

2450-413: Is a mathematical model of spacetime in which the notion of distance between points (the metric ) is different from the notion of distance in ordinary Euclidean geometry . It is closely related to hyperbolic space , which can be viewed as a disk as illustrated on the right. This image shows a tessellation of a disk by triangles and squares. One can define the distance between points of this disk in such

2548-416: Is equivalent to the conformal field theory known as Liouville field theory . Another conjecture formulated by Edward Witten states that three-dimensional gravity in anti-de Sitter space is equivalent to a conformal field theory with monster group symmetry. These conjectures provide examples of the AdS/CFT correspondence that do not require the full apparatus of string or M-theory. Unlike our universe, which

2646-437: Is extremely useful for making predictions, these predictions are only possible when the strength of the interactions, the coupling constant , is small enough to reliably describe the theory as being close to a theory without interactions . The starting point for string theory is the idea that the point-like particles of quantum field theory can also be modeled as one-dimensional objects called strings. The interaction of strings

2744-441: Is formulated in the language of classical physics that was developed by physicists such as Isaac Newton and James Clerk Maxwell . The other nongravitational forces are explained in the framework of quantum mechanics . Developed in the first half of the twentieth century by a number of different physicists, quantum mechanics provides a radically different way of describing physical phenomena based on probability. Quantum gravity

2842-400: Is its boundary (which looks like a cylinder in the case of three-dimensional anti-de Sitter space). One property of this boundary is that, locally around any point, it looks just like Minkowski space , the model of spacetime used in nongravitational physics. One can therefore consider an auxiliary theory in which "spacetime" is given by the boundary of anti-de Sitter space. This observation is

2940-414: Is most straightforwardly defined by generalizing the perturbation theory used in ordinary quantum field theory. At the level of Feynman diagrams, this means replacing the one-dimensional diagram representing the path of a point particle by a two-dimensional surface representing the motion of a string. Unlike in quantum field theory, string theory does not yet have a full non-perturbative definition, so many of

3038-430: Is not QCD ... It has no mass scale and is conformally invariant. It has no confinement and no running coupling constant. It is supersymmetric. It has no chiral symmetry breaking or mass generation. It has six scalar and fermions in the adjoint representation ... It may be possible to correct some or all of the above problems, or, for various physical problems, some of the objections may not be relevant. As yet there

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3136-578: Is not consensus nor compelling arguments for the conjectured fixes or phenomena which would insure that the N = 4 supersymmetric Yang Mills results would reliably reflect QCD. In a letter to Physics Today , Nobel laureate Philip W. Anderson voiced similar concerns about applications of AdS/CFT to condensed matter physics, stating As a very general problem with the AdS/CFT approach in condensed-matter theory, we can point to those telltale initials "CFT"—conformal field theory. Condensed-matter problems are, in general, neither relativistic nor conformal. Near

3234-447: Is now known to be expanding at an accelerating rate, anti-de Sitter space is neither expanding nor contracting. Instead it looks the same at all times. In more technical language, one says that anti-de Sitter space corresponds to a universe with a negative cosmological constant , whereas the real universe has a small positive cosmological constant. Although the properties of gravity at short distances should be somewhat independent of

3332-528: Is one dimension of time. Thus, in the language of modern physics, one says that spacetime is four-dimensional. One peculiar feature of string theory and M-theory is that these theories require extra dimensions of spacetime for their mathematical consistency: in string theory spacetime is ten-dimensional, while in M-theory it is eleven-dimensional. The quantum gravity theories appearing in the AdS/CFT correspondence are typically obtained from string and M-theory by

3430-405: Is some arbitrary number N , rather than three. In this article, 't Hooft considered a certain limit where N tends to infinity and argued that in this limit certain calculations in quantum field theory resemble calculations in string theory. In 1975, Stephen Hawking published a calculation that suggested that black holes are not completely black but emit a dim radiation due to quantum effects near

3528-550: Is the branch of physics that seeks to describe gravity using the principles of quantum mechanics. Currently, a popular approach to quantum gravity is string theory , which models elementary particles not as zero-dimensional points but as one-dimensional objects called strings . In the AdS/CFT correspondence, one typically considers theories of quantum gravity derived from string theory or its modern extension, M-theory . In everyday life, there are three familiar dimensions of space (up/down, left/right, and forward/backward), and there

3626-468: Is usually referred to as unitarity of time evolution. The apparent contradiction between Hawking's calculation and the unitarity postulate of quantum mechanics came to be known as the black hole information paradox . The AdS/CFT correspondence resolves the black hole information paradox, at least to some extent, because it shows how a black hole can evolve in a manner consistent with quantum mechanics in some contexts. Indeed, one can consider black holes in

3724-539: The EPR thought experiment , simple illustrations of time dilation , and so on. These usually lead to real experiments designed to verify that the conclusion (and therefore the assumptions) of the thought experiments are correct. The EPR thought experiment led to the Bell inequalities , which were then tested to various degrees of rigor , leading to the acceptance of the current formulation of quantum mechanics and probabilism as

3822-572: The Scientific Revolution gathered pace, the concepts of matter , energy, space, time and causality slowly began to acquire the form we know today, and other sciences spun off from the rubric of natural philosophy . Thus began the modern era of theory with the Copernican paradigm shift in astronomy, soon followed by Johannes Kepler 's expressions for planetary orbits, which summarized the meticulous observations of Tycho Brahe ;

3920-531: The Yang–Mills theories that describe elementary particles. The duality represents a major advance in the understanding of string theory and quantum gravity. This is because it provides a non-perturbative formulation of string theory with certain boundary conditions and because it is the most successful realization of the holographic principle , an idea in quantum gravity originally proposed by Gerard 't Hooft and promoted by Leonard Susskind . It also provides

4018-443: The extra dimensions of the theory, and in two- or one-dimensional solid state physics , where one considers a system which is limited in one of the three usual spatial dimensions. At the limit where the size of the compact dimension goes to zero, no fields depend on this extra dimension, and the theory is dimensionally reduced . In string theory, compactification is a generalization of Kaluza–Klein theory . It tries to reconcile

AdS/CFT correspondence - Misplaced Pages Continue

4116-603: The quantum mechanical idea that ( action and) energy are not continuously variable. Theoretical physics consists of several different approaches. In this regard, theoretical particle physics forms a good example. For instance: " phenomenologists " might employ ( semi- ) empirical formulas and heuristics to agree with experimental results, often without deep physical understanding . "Modelers" (also called "model-builders") often appear much like phenomenologists, but try to model speculative theories that have certain desirable features (rather than on experimental data), or apply

4214-506: The quarks that make up atomic nuclei to deconfine at temperatures of approximately two trillion kelvins , conditions similar to those present at around 10 seconds after the Big Bang . The physics of the quark–gluon plasma is governed by quantum chromodynamics, but this theory is mathematically intractable in problems involving the quark–gluon plasma. In an article appearing in 2005, Đàm Thanh Sơn and his collaborators showed that

4312-593: The shear viscosity η and volume density of entropy s , should be approximately equal to a certain universal constant : where ħ denotes the reduced Planck constant and k is the Boltzmann constant . In addition, the authors conjectured that this universal constant provides a lower bound for η / s in a large class of systems. In an experiment conducted at the Relativistic Heavy Ion Collider at Brookhaven National Laboratory ,

4410-409: The strong force . It describes particles similar to the gluons of quantum chromodynamics together with certain fermions . As a result, it has found applications in nuclear physics , particularly in the study of the quark–gluon plasma . Another realization of the correspondence states that M-theory on AdS 7 × S is equivalent to the so-called (2,0)-theory in six dimensions. In this example,

4508-461: The two-fluid theory of electricity are two cases in this point. However, an exception to all the above is the wave–particle duality , a theory combining aspects of different, opposing models via the Bohr complementarity principle . Physical theories become accepted if they are able to make correct predictions and no (or few) incorrect ones. The theory should have, at least as a secondary objective,

4606-429: The 19th century. Another important event in the 19th century was the discovery of electromagnetic theory , unifying the previously separate phenomena of electricity, magnetism and light. The pillars of modern physics , and perhaps the most revolutionary theories in the history of physics, have been relativity theory and quantum mechanics . Newtonian mechanics was subsumed under special relativity and Newton's gravity

4704-406: The AdS/CFT correspondence could be used to understand some aspects of the quark–gluon plasma by describing it in the language of string theory. By applying the AdS/CFT correspondence, Sơn and his collaborators were able to describe the quark gluon plasma in terms of black holes in five-dimensional spacetime. The calculation showed that the ratio of two quantities associated with the quark–gluon plasma,

4802-475: The AdS/CFT correspondence has been the AdS5/CFT4 correspondence: a relation between N = 4 supersymmetric Yang–Mills theory in 3+1 dimensions and type IIB superstring theory on AdS 5 × S . Current understanding of gravity is based on Albert Einstein 's general theory of relativity . Formulated in 1915, general relativity explains gravity in terms of the geometry of space and time, or spacetime . It

4900-414: The AdS/CFT correspondence states that type IIB string theory on the product space AdS 5 × S is equivalent to N = 4 supersymmetric Yang–Mills theory on the four-dimensional boundary. In this example, the spacetime on which the gravitational theory lives is effectively five-dimensional (hence the notation AdS 5 ), and there are five additional compact dimensions (encoded by the S factor). In

4998-437: The AdS/CFT correspondence, and he suggested a concrete mechanism by which black holes might preserve information. One physical system that has been studied using the AdS/CFT correspondence is the quark–gluon plasma, an exotic state of matter produced in particle accelerators . This state of matter arises for brief instants when heavy ions such as gold or lead nuclei are collided at high energies. Such collisions cause

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5096-476: The Dutchmen Snell and Huygens. In the 18th and 19th centuries Joseph-Louis Lagrange , Leonhard Euler and William Rowan Hamilton would extend the theory of classical mechanics considerably. They picked up the interactive intertwining of mathematics and physics begun two millennia earlier by Pythagoras. Among the great conceptual achievements of the 19th and 20th centuries were the consolidation of

5194-587: The Earth ) or may be an alternative model that provides answers that are more accurate or that can be more widely applied. In the latter case, a correspondence principle will be required to recover the previously known result . Sometimes though, advances may proceed along different paths. For example, an essentially correct theory may need some conceptual or factual revisions; atomic theory , first postulated millennia ago (by several thinkers in Greece and India ) and

5292-401: The apparent contradiction came to be known as the black hole information paradox. Later, in 1993, Gerard 't Hooft wrote a speculative paper on quantum gravity in which he revisited Hawking's work on black hole thermodynamics , concluding that the total number of degrees of freedom in a region of spacetime surrounding a black hole is proportional to the surface area of the horizon. This idea

5390-419: The applications of relativity to problems in astronomy and cosmology respectively . All of these achievements depended on the theoretical physics as a moving force both to suggest experiments and to consolidate results — often by ingenious application of existing mathematics, or, as in the case of Descartes and Newton (with Leibniz ), by inventing new mathematics. Fourier's studies of heat conduction led to

5488-514: The body of knowledge of both factual and scientific views and possess a usual scientific quality of the tests of repeatability, consistency with existing well-established science and experimentation. There do exist mainstream theories that are generally accepted theories based solely upon their effects explaining a wide variety of data, although the detection, explanation, and possible composition are subjects of debate. The proposed theories of physics are usually relatively new theories which deal with

5586-400: The conformal field theory appearing in the correspondence lives on the boundary of anti-de Sitter space. One special case of Maldacena's proposal says that N = 4 super Yang–Mills theory, a gauge theory similar in some ways to quantum chromodynamics, is equivalent to string theory in five-dimensional anti-de Sitter space. This result helped clarify the earlier work of 't Hooft on

5684-529: The context of string theory, where they are associated with the surface swept out by a string propagating through spacetime, and in statistical mechanics , where they model systems at a thermodynamic critical point . In the AdS/CFT correspondence, one considers string theory or M-theory on an anti-de Sitter background . This means that the geometry of spacetime is described in terms of a certain vacuum solution of Einstein's equation called anti-de Sitter space . In very elementary terms, anti-de Sitter space

5782-467: The context of the AdS/CFT correspondence, and any such black hole corresponds to a configuration of particles on the boundary of anti-de Sitter space. These particles obey the usual rules of quantum mechanics and in particular evolve in a unitary fashion, so the black hole must also evolve in a unitary fashion, respecting the principles of quantum mechanics. In 2005, Hawking announced that the paradox had been settled in favor of information conservation by

5880-520: The correspondence is correct, although so far it has not been rigorously proved . In order to better understand the quantum aspects of gravity in our four-dimensional universe, some physicists have considered a lower-dimensional mathematical model in which spacetime has only two spatial dimensions and one time dimension. In this setting, the mathematics describing the gravitational field simplifies drastically, and one can study quantum gravity using familiar methods from quantum field theory, eliminating

5978-441: The curvature of spacetime A physical theory involves one or more relationships between various measurable quantities. Archimedes realized that a ship floats by displacing its mass of water, Pythagoras understood the relation between the length of a vibrating string and the musical tone it produces. Other examples include entropy as a measure of the uncertainty regarding the positions and motions of unseen particles and

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6076-466: The energy loss of such a quark to the squared distance traveled through the plasma. Calculations based on the AdS/CFT correspondence give the estimated value ^ q ≈ 4 GeV/fm , and the experimental value of ^ q lies in the range 5–15 GeV/fm . Over the decades, experimental condensed matter physicists have discovered a number of exotic states of matter, including superconductors and superfluids . These states are described using

6174-439: The event horizon. This work extended previous results of Jacob Bekenstein who had suggested that black holes have a well-defined entropy. At first, Hawking's result appeared to contradict one of the main postulates of quantum mechanics, namely the unitarity of time evolution. Intuitively, the unitarity postulate says that quantum mechanical systems do not destroy information as they evolve from one state to another. For this reason,

6272-404: The experimental result in one model was close to this universal constant but it was not the case in another model. Another important property of the quark–gluon plasma is that very high energy quarks moving through the plasma are stopped or "quenched" after traveling only a few femtometres . This phenomenon is characterized by a number ^ q called the jet quenching parameter, which relates

6370-421: The formalism of quantum field theory, but some phenomena are difficult to explain using standard field theoretic techniques. Some condensed matter theorists including Subir Sachdev hope that the AdS/CFT correspondence will make it possible to describe these systems in the language of string theory and learn more about their behavior. So far some success has been achieved in using string theory methods to describe

6468-450: The fundamental fields. Quantum field theories are also used throughout condensed matter physics to model particle-like objects called quasiparticles . In the AdS/CFT correspondence, one considers, in addition to a theory of quantum gravity, a certain kind of quantum field theory called a conformal field theory . This is a particularly symmetric and mathematically well behaved type of quantum field theory. Such theories are often studied in

6566-509: The gap between the conception of our universe based on its four observable dimensions with the ten, eleven, or twenty-six dimensions which theoretical equations lead us to suppose the universe is made with. For this purpose it is assumed the extra dimensions are "wrapped" up on themselves, or "curled" up on Calabi–Yau spaces , or on orbifolds . Models in which the compact directions support fluxes are known as flux compactifications . The coupling constant of string theory , which determines

6664-585: The higher-dimensional quantum gravity theory. Following Maldacena's insight in 1997, theorists have discovered many different realizations of the AdS/CFT correspondence. These relate various conformal field theories to compactifications of string theory and M-theory in various numbers of dimensions. The theories involved are generally not viable models of the real world, but they have certain features, such as their particle content or high degree of symmetry, which make them useful for solving problems in quantum field theory and quantum gravity. The most famous example of

6762-416: The highest order, writing Principia Mathematica . In it contained a grand synthesis of the work of Copernicus, Galileo and Kepler; as well as Newton's theories of mechanics and gravitation, which held sway as worldviews until the early 20th century. Simultaneously, progress was also made in optics (in particular colour theory and the ancient science of geometrical optics ), courtesy of Newton, Descartes and

6860-455: The hose, one discovers that it contains a second dimension, its circumference. Thus, an ant crawling inside it would move in two dimensions. The application of quantum mechanics to physical objects such as the electromagnetic field , which are extended in space and time, is known as quantum field theory . In particle physics , quantum field theories form the basis for our understanding of elementary particles, which are modeled as excitations in

6958-690: The hyperbolic disk. Time runs along the vertical direction in this picture. The surface of this cylinder plays an important role in the AdS/CFT correspondence. As with the hyperbolic plane, anti-de Sitter space is curved in such a way that any point in the interior is actually infinitely far from this boundary surface. This construction describes a hypothetical universe with only two space and one time dimension, but it can be generalized to any number of dimensions. Indeed, hyperbolic space can have more than two dimensions and one can "stack up" copies of hyperbolic space to get higher-dimensional models of anti-de Sitter space. An important feature of anti-de Sitter space

7056-455: The idea of energy (as well as its global conservation) by the inclusion of heat , electricity and magnetism , and then light . The laws of thermodynamics , and most importantly the introduction of the singular concept of entropy began to provide a macroscopic explanation for the properties of matter. Statistical mechanics (followed by statistical physics and Quantum statistical mechanics ) emerged as an offshoot of thermodynamics late in

7154-570: The interplay between experimental studies and theory . In some cases, theoretical physics adheres to standards of mathematical rigour while giving little weight to experiments and observations. For example, while developing special relativity , Albert Einstein was concerned with the Lorentz transformation which left Maxwell's equations invariant, but was apparently uninterested in the Michelson–Morley experiment on Earth 's drift through

7252-675: The late 1920s. In the aftermath of World War 2, more progress brought much renewed interest in QFT, which had since the early efforts, stagnated. The same period also saw fresh attacks on the problems of superconductivity and phase transitions, as well as the first applications of QFT in the area of theoretical condensed matter. The 1960s and 70s saw the formulation of the Standard model of particle physics using QFT and progress in condensed matter physics (theoretical foundations of superconductivity and critical phenomena , among others ), in parallel to

7350-456: The need for string theory or other more radical approaches to quantum gravity in four dimensions. Beginning with the work of J. David Brown and Marc Henneaux in 1986, physicists have noticed that quantum gravity in a three-dimensional spacetime is closely related to two-dimensional conformal field theory. In 1995, Henneaux and his coworkers explored this relationship in more detail, suggesting that three-dimensional gravity in anti-de Sitter space

7448-417: The other phases . This behavior has recently been understood by considering a dual description where properties of the fluid are described in terms of a higher dimensional black hole. With many physicists turning towards string-based methods to solve problems in nuclear and condensed matter physics, some theorists working in these areas have expressed doubts about whether the AdS/CFT correspondence can provide

7546-407: The probabilities of various physical events using the techniques of perturbation theory . Developed by Richard Feynman and others in the first half of the twentieth century, perturbative quantum field theory uses special diagrams called Feynman diagrams to organize computations. One imagines that these diagrams depict the paths of point-like particles and their interactions. Although this formalism

7644-429: The probability of strings splitting and reconnecting, can be described by a field called a dilaton . This in turn can be described as the size of an extra (eleventh) dimension which is compact. In this way, the ten-dimensional type IIA string theory can be described as the compactification of M-theory in eleven dimensions. Furthermore, different versions of string theory are related by different compactifications in

7742-419: The process of becoming established and some proposed theories. It can include speculative sciences. This includes physics fields and physical theories presented in accordance with known evidence, and a body of associated predictions have been made according to that theory. Some fringe theories go on to become a widely accepted part of physics. Other fringe theories end up being disproven. Some fringe theories are

7840-422: The real world, spacetime is four-dimensional, at least macroscopically, so this version of the correspondence does not provide a realistic model of gravity. Likewise, the dual theory is not a viable model of any real-world system as it assumes a large amount of supersymmetry . Nevertheless, as explained below, this boundary theory shares some features in common with quantum chromodynamics , the fundamental theory of

7938-490: The relationship between string theory and quantum chromodynamics, taking string theory back to its roots as a theory of nuclear physics. Maldacena's results also provided a concrete realization of the holographic principle with important implications for quantum gravity and black hole physics. By the year 2015, Maldacena's paper had become the most highly cited paper in high energy physics with over 10,000 citations. These subsequent articles have provided considerable evidence that

8036-607: The rise of medieval universities , the only acknowledged intellectual disciplines were the seven liberal arts of the Trivium like grammar , logic , and rhetoric and of the Quadrivium like arithmetic , geometry , music and astronomy . During the Middle Ages and Renaissance , the concept of experimental science, the counterpoint to theory, began with scholars such as Ibn al-Haytham and Francis Bacon . As

8134-427: The spacetime of the gravitational theory is effectively seven-dimensional. The existence of the (2,0)-theory that appears on one side of the duality is predicted by the classification of superconformal field theories . It is still poorly understood because it is a quantum mechanical theory without a classical limit . Despite the inherent difficulty in studying this theory, it is considered to be an interesting object for

8232-439: The starting point for the AdS/CFT correspondence, which states that the boundary of anti-de Sitter space can be regarded as the "spacetime" for a conformal field theory. The claim is that this conformal field theory is equivalent to the gravitational theory on the bulk anti-de Sitter space in the sense that there is a "dictionary" for translating calculations in one theory into calculations in the other. Every entity in one theory has

8330-403: The string theory approach was abandoned in favor of quantum chromodynamics. In quantum chromodynamics, quarks have a kind of charge that comes in three varieties called colors . In a paper from 1974, Gerard 't Hooft studied the relationship between string theory and nuclear physics from another point of view by considering theories similar to quantum chromodynamics, where the number of colors

8428-484: The study of physics which include scientific approaches, means for determining the validity of models and new types of reasoning used to arrive at the theory. However, some proposed theories include theories that have been around for decades and have eluded methods of discovery and testing. Proposed theories can include fringe theories in the process of becoming established (and, sometimes, gaining wider acceptance). Proposed theories usually have not been tested. In addition to

8526-443: The techniques of mathematical modeling to physics problems. Some attempt to create approximate theories, called effective theories , because fully developed theories may be regarded as unsolvable or too complicated . Other theorists may try to unify , formalise, reinterpret or generalise extant theories, or create completely new ones altogether. Sometimes the vision provided by pure mathematical systems can provide clues to how

8624-454: The theoretical questions that physicists would like to answer remain out of reach. The problem of developing a non-perturbative formulation of string theory was one of the original motivations for studying the AdS/CFT correspondence. As explained above, the correspondence provides several examples of quantum field theories that are equivalent to string theory on anti-de Sitter space. One can alternatively view this correspondence as providing

8722-472: The theories like those listed below, there are also different interpretations of quantum mechanics , which may or may not be considered different theories since it is debatable whether they yield different predictions for physical experiments, even in principle. For example, AdS/CFT correspondence , Chern–Simons theory , graviton , magnetic monopole , string theory , theory of everything . Fringe theories include any new area of scientific endeavor in

8820-492: The tools needed to realistically model real-world systems. In a talk at the Quark Matter conference in 2006, an American physicist, Larry McLerran pointed out that the N = 4 super Yang–Mills theory that appears in the AdS/CFT correspondence differs significantly from quantum chromodynamics, making it difficult to apply these methods to nuclear physics. According to McLerran, N  = 4 supersymmetric Yang–Mills

8918-418: The transition of a superfluid to an insulator . A superfluid is a system of electrically neutral atoms that flows without any friction . Such systems are often produced in the laboratory using liquid helium , but recently experimentalists have developed new ways of producing artificial superfluids by pouring trillions of cold atoms into a lattice of criss-crossing lasers . These atoms initially behave as

9016-452: The value of the cosmological constant, it is desirable to have a version of the AdS/CFT correspondence for positive cosmological constant. In 2001, Andrew Strominger introduced a version of the duality called the dS/CFT correspondence . This duality involves a model of spacetime called de Sitter space with a positive cosmological constant. Such a duality is interesting from the point of view of cosmology since many cosmologists believe that

9114-478: The very early universe was close to being de Sitter space. Although the AdS/CFT correspondence is often useful for studying the properties of black holes, most of the black holes considered in the context of AdS/CFT are physically unrealistic. Indeed, as explained above, most versions of the AdS/CFT correspondence involve higher-dimensional models of spacetime with unphysical supersymmetry. Theoretical physics The advancement of science generally depends on

9212-530: The works of these men (alongside Galileo's) can perhaps be considered to constitute the Scientific Revolution. The great push toward the modern concept of explanation started with Galileo , one of the few physicists who was both a consummate theoretician and a great experimentalist . The analytic geometry and mechanics of Descartes were incorporated into the calculus and mechanics of Isaac Newton , another theoretician/experimentalist of

9310-405: Was first proposed by Juan Maldacena in late 1997. Important aspects of the correspondence were soon elaborated on in two articles, one by Steven Gubser , Igor Klebanov and Alexander Polyakov , and another by Edward Witten . By 2015, Maldacena's article had over 10,000 citations, becoming the most highly cited article in the field of high energy physics . One of the most prominent examples of

9408-422: Was given a kinematic explanation by general relativity . Quantum mechanics led to an understanding of blackbody radiation (which indeed, was an original motivation for the theory) and of anomalies in the specific heats of solids — and finally to an understanding of the internal structures of atoms and molecules . Quantum mechanics soon gave way to the formulation of quantum field theory (QFT), begun in

9506-434: Was promoted by Leonard Susskind and is now known as the holographic principle . The holographic principle and its realization in string theory through the AdS/CFT correspondence have helped elucidate the mysteries of black holes suggested by Hawking's work and are believed to provide a resolution of the black hole information paradox. In 2004, Hawking conceded that black holes do not violate quantum mechanics, and he suggested

9604-409: Was the culmination of a long history of efforts to relate string theory to nuclear physics. In fact, string theory was originally developed during the late 1960s and early 1970s as a theory of hadrons , the subatomic particles like the proton and neutron that are held together by the strong nuclear force . The idea was that each of these particles could be viewed as a different oscillation mode of

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