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AGT Correspondence
In theoretical physics, the AGT correspondence is a relationship between Liouville field theory on a punctured Riemann surface and a certain four-dimensional SU(2) gauge theory obtained by compactifying the 6D (2,0) superconformal field theory on the surface. The relationship was discovered by Luis Alday, Davide Gaiotto, and Yuji Tachikawa in 2009. It was soon extended to a more general relationship between AN-1 Toda field theory In mathematics and physics, specifically the study of field theory and partial differential equations, a Toda field theory, named after Morikazu Toda, is specified by a choice of Kac–Moody algebra and a specific Lagrangian. Fixing the Kac–Mo ... and SU(N) gauge theories. The idea of the AGT correspondence has also been extended to describe relationships between three-dimensional theories.Dimofte, Gaiotto, Gukov 2010 Notes References * * * Conformal field theory Gauge theories String theory {{string-theory-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theoretical Physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experimental tools to probe these phenomena. The advancement of science generally depends on 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.There is some debate as to whether or not theoretical physics uses mathematics to build intuition and illustrativeness to extract physical insight (especially when normal experience fails), rather than as a tool in formalizing theories. This links to the question of it using mathematics in a less formally rigorous, and more intuitive or heuristic way than, say, mathematical physics. For example, while developing special relativity, Albert Einstein was concerned wit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Liouville Field Theory
In physics, Liouville field theory (or simply Liouville theory) is a two-dimensional conformal field theory whose classical equation of motion is a generalization of Liouville's equation. Liouville theory is defined for all complex values of the central charge c of its Virasoro symmetry algebra, but it is unitary only if :c\in(1,+\infty), and its classical limit is : c\to +\infty. Although it is an interacting theory with a continuous spectrum, Liouville theory has been solved. In particular, its three-point function on the sphere has been determined analytically. Introduction Liouville theory describes the dynamics of a field \phi called the Liouville field, which is defined on a two-dimensional space. This field is not a free field due to the presence of an exponential potential : V(\phi) = e^\ , where the parameter b is called the coupling constant. In a free field theory, the energy eigenvectors e^ are linearly independent, and the momentum \alpha is conserved in intera ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Riemann Surface
In mathematics, particularly in complex analysis, a Riemann surface is a connected one-dimensional complex manifold. These surfaces were first studied by and are named after Bernhard Riemann. Riemann surfaces can be thought of as deformed versions of the complex plane: locally near every point they look like patches of the complex plane, but the global topology can be quite different. For example, they can look like a sphere or a torus or several sheets glued together. The main interest in Riemann surfaces is that holomorphic functions may be defined between them. Riemann surfaces are nowadays considered the natural setting for studying the global behavior of these functions, especially multi-valued functions such as the square root and other algebraic functions, or the logarithm. Every Riemann surface is a two-dimensional real analytic manifold (i.e., a surface), but it contains more structure (specifically a complex structure) which is needed for the unambiguous definitio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Special Unitary Group
In mathematics, the special unitary group of degree , denoted , is the Lie group of unitary matrices with determinant 1. The more general unitary matrices may have complex determinants with absolute value 1, rather than real 1 in the special case. The group operation is matrix multiplication. The special unitary group is a normal subgroup of the unitary group , consisting of all unitary matrices. As a compact classical group, is the group that preserves the standard inner product on \mathbb^n. It is itself a subgroup of the general linear group, \operatorname(n) \subset \operatorname(n) \subset \operatorname(n, \mathbb ). The groups find wide application in the Standard Model of particle physics, especially in the electroweak interaction and in quantum chromodynamics. The groups are important in quantum computing, as they represent the possible quantum logic gate operations in a quantum circuit with n qubits and thus 2^n basis states. (Alternatively, the more genera ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gauge Theory
In physics, a gauge theory is a type of field theory in which the Lagrangian (and hence the dynamics of the system itself) does not change (is invariant) under local transformations according to certain smooth families of operations (Lie groups). The term ''gauge'' refers to any specific mathematical formalism to regulate redundant degrees of freedom in the Lagrangian of a physical system. The transformations between possible gauges, called ''gauge transformations'', form a Lie group—referred to as the ''symmetry group'' or the ''gauge group'' of the theory. Associated with any Lie group is the Lie algebra of group generators. For each group generator there necessarily arises a corresponding field (usually a vector field) called the ''gauge field''. Gauge fields are included in the Lagrangian to ensure its invariance under the local group transformations (called ''gauge invariance''). When such a theory is quantized, the quanta of the gauge fields are called '' gauge bosons ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
6D (2,0) Superconformal Field Theory
In theoretical physics, the six-dimensional (2,0)-superconformal field theory is a quantum field theory whose existence is predicted by arguments in string theory. It is still poorly understood because there is no known description of the theory in terms of an action functional. Despite the inherent difficulty in studying this theory, it is considered to be an interesting object for a variety of reasons, both physical and mathematical. Applications The (2,0)-theory has proven to be important for studying the general properties of quantum field theories. Indeed, this theory subsumes a large number of mathematically interesting effective quantum field theories and points to new dualities relating these theories. For example, Luis Alday, Davide Gaiotto, and Yuji Tachikawa showed that by compactifying this theory on a surface, one obtains a four-dimensional quantum field theory, and there is a duality known as the AGT correspondence which relates the physics of this theory to cert ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Davide Gaiotto
Davide Silvano Achille Gaiotto (born 11 March 1977) is an Italian mathematical physicist who deals with quantum field theories and string theory. He received the Gribov Medal in 2011 and the New Horizons in Physics Prize in 2013. Biography Gaiotto won 1996 the silver medal as Italian participants in the International Mathematical Olympiad and 1995 gold medal at the International Physics Olympiad in Canberra. He was an undergraduate student at Scuola Normale Superiore in Pisa from 1996 to 2000. From 2004 to 2007 he was a post-doctoral researcher at Harvard University and then to 2011 the Institute for Advanced Study. Since 2011 he has been working at the Perimeter Institute for Theoretical Physics in Waterloo, Ontario. He introduced new techniques in the study and design of four-dimensional (N = 2) supersymmetric conformal field theories. He constructed from M5-branes, which are wound around Riemann surfaces with punctures. This led to new insights into the dynamics of four-dimen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Toda Field Theory
In mathematics and physics, specifically the study of field theory and partial differential equations, a Toda field theory, named after Morikazu Toda, is specified by a choice of Kac–Moody algebra and a specific Lagrangian. Fixing the Kac–Moody algebra to have rank r, that is, the Cartan subalgebra of the algebra has dimension r, the Lagrangian can be written \mathcal=\frac\left\langle \partial_\mu \phi, \partial^\mu \phi \right\rangle -\frac\sum_^r n_i \exp(\beta \langle\alpha_i, \phi\rangle). The background spacetime is 2-dimensional Minkowski space, with space-like coordinate x and timelike coordinate t. Greek indices indicate spacetime coordinates. For some choice of root basis, \alpha_i is the ith simple root. This provides a basis for the Cartan subalgebra, allowing it to be identified with \mathbb^r. Then the field content is a collection of r scalar fields \phi_i, which are scalar in the sense that they transform trivially under Lorentz transformations of the under ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Letters In Mathematical Physics
''Letters in Mathematical Physics'' is a peer-reviewed scientific journal in mathematical physics published by Springer Science+Business Media. It publishes letters and longer research articles, occasionally also articles containing topical reviews. It is essentially a platform for the rapid dissemination of short contributions in the field of mathematical physics. In addition, the journal publishes contributions to modern mathematics in fields which have a potential physical application, and developments in theoretical physics which have potential mathematical impact. The editors are Volker Bach, Edward Frenkel, Maxim Kontsevich, Dirk Kreimer, Nikita Nekrasov, Massimo Porrati, and Daniel Sternheimer. Abstracting and indexing The following services abstract or index ''Letters in Mathematical Physics'': Academic OneFile, Academic Search, Astrophysics Data System, Chemical Abstracts Service, Current Contents/Physical, Chemical and Earth Sciences, Current Index to Statistics, EBSC ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of High Energy Physics
The ''Journal of High Energy Physics'' is a monthly peer-reviewed open access scientific journal covering the field of high energy physics. It is published by Springer Science+Business Media on behalf of the International School for Advanced Studies. The journal is part of the SCOAP3 initiative. According to the ''Journal Citation Reports'', the journal has a 2020 impact factor of 5.810. References External links *Journal pageat International School for Advanced Studies The International School for Advanced Studies (Italian: ''Scuola Internazionale Superiore di Studi Avanzati''; SISSA) is an international, state-supported, post-graduate-education and research institute in Trieste, Italy. SISSA is active in th ... website English-language journals Monthly journals Physics journals Publications established in 1997 Springer Science+Business Media academic journals Academic journals associated with learned and professional societies Particle physics journals {{p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Communications In Mathematical Physics
''Communications in Mathematical Physics'' is a peer-reviewed academic journal published by Springer. The journal publishes papers in all fields of mathematical physics, but focuses particularly in analysis related to condensed matter physics, statistical mechanics and quantum field theory, and in operator algebras, quantum information and relativity. History Rudolf Haag conceived this journal with Res Jost, and Haag became the Founding Chief Editor. The first issue of ''Communications in Mathematical Physics'' appeared in 1965. Haag guided the journal for the next eight years. Then Klaus Hepp succeeded him for three years, followed by James Glimm, for another three years. Arthur Jaffe began as chief editor in 1979 and served for 21 years. Michael Aizenman became the fifth chief editor in the year 2000 and served in this role until 2012. The current editor-in-chief is Horng-Tzer Yau. Archives Articles from 1965 to 1997 are available in electronic form free of charge, via Pro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conformal Field Theory
A conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations. In two dimensions, there is an infinite-dimensional algebra of local conformal transformations, and conformal field theories can sometimes be exactly solved or classified. Conformal field theory has important applications to condensed matter physics, statistical mechanics, quantum statistical mechanics, and string theory. Statistical and condensed matter systems are indeed often conformally invariant at their thermodynamic or quantum critical points. Scale invariance vs conformal invariance In quantum field theory, scale invariance is a common and natural symmetry, because any fixed point of the renormalization group is by definition scale invariant. Conformal symmetry is stronger than scale invariance, and one needs additional assumptions to argue that it should appear in nature. The basic idea behind its plausibility is that ''local'' scale invariant theories have their ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
