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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] |
Quantum Field Theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and in condensed matter physics to construct models of quasiparticles. QFT treats particles as excited states (also called quanta) of their underlying quantum fields, which are more fundamental than the particles. The equation of motion of the particle is determined by minimization of the Lagrangian, a functional of fields associated with the particle. Interactions between particles are described by interaction terms in the Lagrangian involving their corresponding quantum fields. Each interaction can be visually represented by Feynman diagrams according to perturbation theory in quantum mechanics. History Quantum field theory emerged from the work of generations of theoretical physicists spanning much of the 20th century. Its devel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mikhail Khovanov
Mikhail Khovanov (russian: Михаил Гелиевич Хованов; born 1972) is a Russian- American professor of mathematics at Columbia University who works on representation theory, knot theory, and algebraic topology. He is known for introducing Khovanov homology for links, which was one of the first examples of categorification. Education and career Khovanov graduated from Moscow State School 57 mathematical class in 1988. He earned a PhD in mathematics from Yale University in 1997, where he studied under Igor Frenkel. Khovanov was a faculty member at UC Davis The University of California, Davis (UC Davis, UCD, or Davis) is a Public university, public Land-grant university, land-grant research university near Davis, California. Named a Public Ivy, it is the northernmost of the ten campuses of the Uni ... before moving to Columbia University. [...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 t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Advances In Mathematics
''Advances in Mathematics'' is a peer-reviewed scientific journal covering research on pure mathematics. It was established in 1961 by Gian-Carlo Rota. The journal publishes 18 issues each year, in three volumes. At the origin, the journal aimed at publishing articles addressed to a broader "mathematical community", and not only to mathematicians in the author's field. Herbert Busemann writes, in the preface of the first issue, "The need for expository articles addressing either all mathematicians or only those in somewhat related fields has long been felt, but little has been done outside of the USSR. The serial publication ''Advances in Mathematics'' was created in response to this demand." Abstracting and indexing The journal is abstracted and indexed in: * [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
N = 4 Supersymmetric Yang–Mills Theory
''N'' = 4 supersymmetric Yang–Mills (SYM) theory is a mathematical and physical model created to study particles through a simple system, similar to string theory, with conformal symmetry. It is a simplified toy theory based on Yang–Mills theory that does not describe the real world, but is useful because it can act as a proving ground for approaches for attacking problems in more complex theories. It describes a universe containing boson fields and fermion fields which are related by four supersymmetries (this means that swapping boson, fermion and scalar fields in a certain way leaves the predictions of the theory invariant). It is one of the simplest (because it has no free parameters except for the gauge group) and one of the few finite quantum field theories in 4 dimensions. It can be thought of as the most symmetric field theory that does not involve gravity. Meaning of ''N'' and numbers of fields In ''N'' supersymmetric Yang–Mills theory, ''N'' denotes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ABJM Superconformal Field Theory
In theoretical physics, ABJM theory is a quantum field theory studied by Ofer Aharony, Oren Bergman, Daniel Jafferis, and Juan Maldacena. It provides a holographic dual to M-theory on AdS_4\times S^7. The ABJM theory is also closely related to Chern–Simons theory The Chern–Simons theory is a 3-dimensional topological quantum field theory of Schwarz type developed by Edward Witten. It was discovered first by mathematical physicist Albert Schwarz. It is named after mathematicians Shiing-Shen Chern and Jam ..., and it serves as a useful toy model for solving problems that arise in condensed matter physics.Aharony et al. 2008 It is a theory defined on d = 3, \mathcal = 6 superspace. See also * 6D (2,0) superconformal field theory Notes References * * Conformal field theory Supersymmetric quantum field theory String theory {{string-theory-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyperkähler Manifold
In differential geometry, a hyperkähler manifold is a Riemannian manifold (M, g) endowed with three integrable almost complex structures I, J, K that are Kähler with respect to the Riemannian metric g and satisfy the quaternionic relations I^2=J^2=K^2=IJK=-1. In particular, it is a hypercomplex manifold. All hyperkähler manifolds are Ricci-flat and are thus Calabi–Yau manifolds. Hyperkähler manifolds were defined by Eugenio Calabi in 1979. Equivalent definition in terms of holonomy Equivalently, a hyperkähler manifold is a Riemannian manifold (M, g) of dimension 4n whose holonomy group is contained in the compact symplectic group . Indeed, if (M, g, I, J, K) is a hyperkähler manifold, then the tangent space is a quaternionic vector space for each point of , i.e. it is isomorphic to \mathbb^n for some integer n, where \mathbb is the algebra of quaternions. The compact symplectic group can be considered as the group of orthogonal transformations of \mathbb^n w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Andrew Neitzke
Andrew Neitzke is an American mathematician and theoretical physicist, at Yale University. He works in mathematical physics, mainly in geometric problems arising from physics, particularly from supersymmetric quantum field theory. Education and career Neitzke earned his AB at Princeton University as valedictorian. After one year as a Marshall Scholar for Part III of the Mathematical Tripos at the University of Cambridge, he earned his doctorate in 2005 at Harvard University under the supervision of Cumrun Vafa. After postdoctoral research at the Institute for Advanced Study and Harvard University, he became an assistant professor at the University of Texas at Austin in 2009, and was promoted to full professor by 2019. He moved to Yale University in 2020, at first as associate professor but later in 2020 becoming full professor again. Recognition In 2018, he became a fellow of the American Mathematical Society The American Mathematical Society (AMS) is an association of pro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greg Moore (physicist)
Gregory W. Moore is an American theoretical physicist who specializes in mathematical physics and string theory. Moore is a professor in the Physics and Astronomy Department of Rutgers University and a member of the University's High Energy Theory group. Education Moore received an AB in physics from Princeton University in 1982 and a PhD in the same subject from Harvard University in 1985. Career Moore's research has focused on: D-branes on Calabi–Yau manifolds and BPS state counting; relations to Borcherds products, automorphic forms, black-hole entropy, and wall-crossing; applications of the theory of automorphic forms to conformal field theory, string compactification, black hole entropy counting, and the AdS/CFT correspondence; potential relation between string theory and number theory; effective low energy supergravity theories in string compactification and the computation of nonperturbative stringy effects in effective supergravities; topological field theories, and a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Knot Theory
In the mathematical field of topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined so it cannot be undone, the simplest knot being a ring (or "unknot"). In mathematical language, a knot is an embedding of a circle in 3-dimensional Euclidean space, \mathbb^3 (in topology, a circle is not bound to the classical geometric concept, but to all of its homeomorphisms). Two mathematical knots are equivalent if one can be transformed into the other via a deformation of \mathbb^3 upon itself (known as an ambient isotopy); these transformations correspond to manipulations of a knotted string that do not involve cutting it or passing through itself. Knots can be described in various ways. Using different description methods, there may be more than one description of the same knot. For example, a common method of describing a knot is a planar d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Khovanov Homology
In mathematics, Khovanov homology is an oriented link invariant that arises as the cohomology of a cochain complex. It may be regarded as a categorification of the Jones polynomial. It was developed in the late 1990s by Mikhail Khovanov, then at the University of California, Davis, now at Columbia University. Overview To any link diagram ''D'' representing a link ''L'', we assign the Khovanov bracket ''D''">/nowiki>''D''/nowiki>, a cochain complex of graded vector spaces. This is the analogue of the Kauffman bracket in the construction of the Jones polynomial. Next, we normalise ''D''">/nowiki>''D''/nowiki> by a series of degree shifts (in the graded vector spaces) and height shifts (in the cochain complex) to obtain a new cochain complex C(''D''). The cohomology of this cochain complex turns out to be an invariant of ''L'', and its graded Euler characteristic is the Jones polynomial of ''L''. Definition This definition follows the formalism given in Dror Bar-Natan's 2002 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
String Theory
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and interact with each other. On distance scales larger than the string scale, a string looks just like an ordinary particle, with its mass, charge, and other properties determined by the vibrational state of the string. In string theory, one of the many vibrational states of the string corresponds to the graviton, a quantum mechanical particle that carries the gravitational force. Thus, string theory is a theory of quantum gravity. String theory is a broad and varied subject that attempts to address a number of deep questions of fundamental physics. String theory has contributed a number of advances to mathematical physics, which have been applied to a variety of problems in black hole physics, early universe cosmology, nuclear physics, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
