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Seiberg–Witten Theory
In theoretical physics, Seiberg–Witten theory is a theory that determines an exact low-energy effective action (for massless degrees of freedom) of a \mathcal = 2 supersymmetric gauge theory—namely the metric of the moduli space of vacua. Seiberg–Witten curves In general, effective Lagrangians of supersymmetric gauge theories are largely determined by their holomorphic properties and their behavior near the singularities. In particular, in gauge theory with \mathcal = 2 extended supersymmetry, the moduli space of vacua is a special Kähler manifold and its Kähler potential is constrained by above conditions. In the original approach, by Seiberg and Witten, holomorphy and electric-magnetic duality constraints are strong enough to almost uniquely constrain the prepotential, and therefore the metric of the moduli space of vacua, for theories with SU(2) gauge group. More generally, consider the example with gauge group SU(n). The classical potential is This vanishes ... [...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] |
Eric D'Hoker
Eric D’Hoker (born 18 October 1956 in Belgium) is a Belgian-American theoretical physicist. Biography D’Hoker studied from 1974 to 1975 at Paris 13 University in Orsay, from 1975 to 1976 at the Lycée Condorcet, and from 1976 to 1978 at the École Polytechnique. In 1978 he became a graduate student in physics at Princeton University, where in 1981 he received his Ph.D. with future Nobel Laureate David Gross as his advisor. As a postdoc, D'Hoker worked from 1981 to 1984 at the Center for Theoretical Physics at Massachusetts Institute of Technology. He then worked an assistant professor from 1984 to 1986 at Columbia University and from 1986 to 1988 at Princeton University. In 1988, D'Hoker became an associate professor at the University of California, Los Angeles (UCLA). He was appointed a full professor in 1990 and a distinguished professor in 2009. From the 1980s onwards, he collaborated extensively with mathematician Duong H. Phong on the geometry underlying superstring pertu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Giotto Duality
Giotto di Bondone (; – January 8, 1337), known mononymously as Giotto ( , ) and Latinised as Giottus, was an Italian painter and architect from Florence during the Late Middle Ages. He worked during the Gothic/Proto-Renaissance period. Giotto's contemporary, the banker and chronicler Giovanni Villani, wrote that Giotto was "the most sovereign master of painting in his time, who drew all his figures and their postures according to nature" and of his publicly recognized "talent and excellence".Bartlett, Kenneth R. (1992). ''The Civilization of the Italian Renaissance''. Toronto: D.C. Heath and Company. (Paperback). p. 37. Giorgio Vasari described Giotto as making a decisive break with the prevalent Byzantine style and as initiating "the great art of painting as we know it today, introducing the technique of drawing accurately from life, which had been neglected for more than two hundred years".Giorgio Vasari, ''Lives of the Artists'', trans. George Bull, Penguin Classics, (196 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Donaldson Theory
In mathematics, and especially gauge theory, Donaldson theory is the study of the topology of smooth 4-manifolds using moduli spaces of anti-self-dual instantons. It was started by Simon Donaldson (1983) who proved Donaldson's theorem restricting the possible quadratic forms on the second cohomology group of a compact simply connected 4-manifold. Important consequences of this theorem include the existence of an Exotic R4 and the failure of the smooth h-cobordism theorem in 4 dimensions. The results of Donaldson theory depend therefore on the manifold having a differential structure, and are largely false for topological 4-manifolds. Many of the theorems in Donaldson theory can now be proved more easily using Seiberg–Witten theory, though there are a number of open problems remaining in Donaldson theory, such as the Witten conjecture and the Atiyah–Floer conjecture. See also * Kronheimer–Mrowka basic class * Instanton * Floer homology * Yang–Mills equations In physi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ginzburg–Landau Theory
In physics, Ginzburg–Landau theory, often called Landau–Ginzburg theory, named after Vitaly Ginzburg and Lev Landau, is a mathematical physical theory used to describe superconductivity. In its initial form, it was postulated as a phenomenological model which could describe type-I superconductors without examining their microscopic properties. One GL-type superconductor is the famous YBCO, and generally all Cuprates. Later, a version of Ginzburg–Landau theory was derived from the Bardeen–Cooper–Schrieffer microscopic theory by Lev Gor'kov, thus showing that it also appears in some limit of microscopic theory and giving microscopic interpretation of all its parameters. The theory can also be given a general geometric setting, placing it in the context of Riemannian geometry, where in many cases exact solutions can be given. This general setting then extends to quantum field theory and string theory, again owing to its solvability, and its close relation to other, simi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Supersymmetric Gauge Theory
In theoretical physics, there are many theories with supersymmetry (SUSY) which also have internal gauge symmetry, gauge symmetries. Supersymmetric gauge theory generalizes this notion. Gauge theory A gauge theory is a mathematical framework for analysing gauge symmetries. There are two types of symmetries, viz., global and local. A global symmetry is the symmetry which remains invariant at each point of a manifold (manifold can be either of spacetime coordinates or that of internal quantum numbers). A local symmetry is the symmetry which depends upon the space over which it is defined, and changes with the variation in coordinates. Thus, such symmetry is invariant only locally (i.e., in a neighborhood on the manifold). Quantum chromodynamics and quantum electrodynamics are famous examples of gauge theories. Supersymmetry In particle physics, there exist particles with two kinds of particle statistics, bosons and fermions. Bosons carry integer spin values, and are characterize ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nikita Nekrasov
Nikita Alexandrovich Nekrasov (russian: Ники́та Алекса́ндрович Некра́сов; born 10 April 1973) is a mathematical and theoretical physicist at the Simons Center for Geometry and Physics and C.N.Yang Institute for Theoretical Physics at Stony Brook University in New York, and a Professor of the Russian Academy of Sciences. Career Nekrasov studied at the Moscow State 57th School in 1986–1989. He graduated with honors from the Moscow Institute of Physics and Technology in 1995, and joined the theory division of the Institute for Theoretical and Experimental Physics. In parallel, in 1994–1996 Nekrasov did his graduate work at Princeton University, under the supervision of David Gross. His Ph.D. thesis on ''Four Dimensional Holomorphic Theories'' was defended in 1996. He joined Harvard Society of Fellows at Harvard University as a Junior Fellow 1996–1999. He was then a Robert. H. Dicke Fellow at Princeton University from 1999 to 2000. In 2000 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hitchin System
In mathematics, the Hitchin integrable system is an integrable system depending on the choice of a complex reductive group and a compact Riemann surface, introduced by Nigel Hitchin in 1987. It lies on the crossroads of algebraic geometry, the theory of Lie algebras and integrable system theory. It also plays an important role in the geometric Langlands correspondence over the field of complex numbers through conformal field theory. A genus zero analogue of the Hitchin system, the Garnier system, was discovered by René Garnier somewhat earlier as a certain limit of the Schlesinger equations, and Garnier solved his system by defining spectral curves. (The Garnier system is the classical limit of the Gaudin model. In turn, the Schlesinger equations are the classical limit of the Knizhnik–Zamolodchikov equations). Almost all integrable systems of classical mechanics can be obtained as particular cases of the Hitchin system or their common generalization defined by Bottacin and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Duong Hong Phong
, birth_date = , birth_place = Nam Dinh, Vietnam , death_date = , death_place = , spouse = , fields = Mathematics , workplaces = Columbia University , alma_mater = , doctoral_students = Paul M. Feehan Richard Wentworth Duong Hong Phong ( vi, Dương Hồng Phong, born 30 August 1953, Nam Dinh, Vietnam) is an American mathematician of Vietnamese origin. He is a professor of mathematics at Columbia University. He is known for his research on complex analysis, partial differential equations, string theory and complex geometry. Education and career After graduating from Lycée Jean-Jacques Rousseau in Saigon, Phong attended a university year at the École Polytechnique Fédérale, Lausanne, Switzerland and then went to the United States as an undergraduate and then a graduate student at Princeton University. In 1977, he defended his dissertation entitled "On Hölder and ''L''''p'' Estimates for the Conjugate Partia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integrable System
In mathematics, integrability is a property of certain dynamical systems. While there are several distinct formal definitions, informally speaking, an integrable system is a dynamical system with sufficiently many conserved quantities, or first integrals, such that its behaviour has far fewer degrees of freedom than the dimensionality of its phase space; that is, its evolution is restricted to a submanifold within its phase space. Three features are often referred to as characterizing integrable systems: * the existence of a ''maximal'' set of conserved quantities (the usual defining property of complete integrability) * the existence of algebraic invariants, having a basis in algebraic geometry (a property known sometimes as algebraic integrability) * the explicit determination of solutions in an explicit functional form (not an intrinsic property, but something often referred to as solvability) Integrable systems may be seen as very different in qualitative character from mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moduli Space
In mathematics, in particular algebraic geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of such objects. Such spaces frequently arise as solutions to classification problems: If one can show that a collection of interesting objects (e.g., the smooth algebraic curves of a fixed genus) can be given the structure of a geometric space, then one can parametrize such objects by introducing coordinates on the resulting space. In this context, the term "modulus" is used synonymously with "parameter"; moduli spaces were first understood as spaces of parameters rather than as spaces of objects. A variant of moduli spaces is formal moduli. Motivation Moduli spaces are spaces of solutions of geometric classification problems. That is, the points of a moduli space correspond to solutions of geometric problems. Here different solutions are identified if they a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
