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Edward Witten
Edward Witten (born August 26, 1951) is an American mathematical and theoretical physicist. He is a Professor Emeritus in the School of Natural Sciences at the Institute for Advanced Study in Princeton. Witten is a researcher in string theory, quantum gravity, supersymmetric quantum field theories, and other areas of mathematical physics. Witten's work has also significantly impacted pure mathematics. In 1990, he became the first physicist to be awarded a Fields Medal by the International Mathematical Union, for his mathematical insights in physics, such as his 1981 proof of the positive energy theorem in general relativity, and his interpretation of the Jones invariants of knots as Feynman integrals. He is considered the practical founder of M-theory.Duff 1998, p. 65 Early life and education Witten was born on August 26, 1951, in Baltimore, Maryland, to a Jewish family. He is the son of Lorraine (née Wollach) Witten and Louis Witten, a theoretical physicist specializing in gr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Baltimore
Baltimore ( , locally: or ) is the most populous city in the U.S. state of Maryland, fourth most populous city in the Mid-Atlantic, and the 30th most populous city in the United States with a population of 585,708 in 2020. Baltimore was designated an independent city by the Constitution of Maryland in 1851, and today is the most populous independent city in the United States. As of 2021, the population of the Baltimore metropolitan area was estimated to be 2,838,327, making it the 20th largest metropolitan area in the country. Baltimore is located about north northeast of Washington, D.C., making it a principal city in the Washington–Baltimore combined statistical area (CSA), the third-largest CSA in the nation, with a 2021 estimated population of 9,946,526. Prior to European colonization, the Baltimore region was used as hunting grounds by the Susquehannock Native Americans, who were primarily settled further northwest than where the city was later built. Co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 vanish ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Witten Conjecture
In algebraic geometry, the Witten conjecture is a conjecture about intersection numbers of stable classes on the moduli space of curves, introduced by Edward Witten in the paper , and generalized in . Witten's original conjecture was proved by Maxim Kontsevich in the paper . Witten's motivation for the conjecture was that two different models of 2-dimensional quantum gravity should have the same partition function. The partition function for one of these models can be described in terms of intersection numbers on the moduli stack of algebraic curves, and the partition function for the other is the logarithm of the τ-function of the KdV hierarchy. Identifying these partition functions gives Witten's conjecture that a certain generating function formed from intersection numbers should satisfy the differential equations of the KdV hierarchy. Statement Suppose that ''M''''g'',''n'' is the moduli stack of compact Riemann surfaces of genus ''g'' with ''n'' distinct marked points ''x' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topological String Theory
In theoretical physics, topological string theory is a version of string theory. Topological string theory appeared in papers by theoretical physicists, such as Edward Witten and Cumrun Vafa, by analogy with Witten's earlier idea of topological quantum field theory. Overview There are two main versions of topological string theory: the topological A-model and the topological B-model. The results of the calculations in topological string theory generically encode all holomorphic quantities within the full string theory whose values are protected by spacetime supersymmetry. Various calculations in topological string theory are closely related to Chern–Simons theory, Gromov–Witten invariants, mirror symmetry, geometric Langlands Program, and many other topics. The operators in topological string theory represent the algebra of operators in the full string theory that preserve a certain amount of supersymmetry. Topological string theory is obtained by a topological twist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topological Quantum Field Theory
In gauge theory and mathematical physics, a topological quantum field theory (or topological field theory or TQFT) is a quantum field theory which computes topological invariants. Although TQFTs were invented by physicists, they are also of mathematical interest, being related to, among other things, knot theory and the theory of four-manifolds in algebraic topology, and to the theory of moduli spaces in algebraic geometry. Donaldson, Jones, Witten, and Kontsevich have all won Fields Medals for mathematical work related to topological field theory. In condensed matter physics, topological quantum field theories are the low-energy effective theories of topologically ordered states, such as fractional quantum Hall states, string-net condensed states, and other strongly correlated quantum liquid states. Overview In a topological field theory, correlation functions do not depend on the metric of spacetime. This means that the theory is not sensitive to changes in the sha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
BCFW Recursion
The Britto–Cachazo–Feng–Witten recursion relations are a set of on-shell recursion relations in quantum field theory. They are named for their creators, Ruth Britto, Freddy Cachazo, Bo Feng and Edward Witten. The BCFW recursion method is a way of calculating scattering amplitude In quantum physics, the scattering amplitude is the probability amplitude of the outgoing spherical wave relative to the incoming plane wave in a stationary-state scattering process. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Witten Index
In quantum field theory and statistical mechanics, the Witten index at the inverse temperature β is defined as a modification of the standard partition function: :\textrm -1)^F e^/math> Note the (-1)F operator, where F is the fermion number operator. This is what makes it different from the ordinary partition function. It is sometimes referred to as the spectral asymmetry. In a supersymmetric theory, each nonzero energy eigenvalue contains an equal number of bosonic and fermionic states. Because of this, the Witten index is independent of the temperature and gives the number of zero energy bosonic vacuum states minus the number of zero energy fermionic vacuum states. In particular, if supersymmetry is spontaneously broken then there are no zero energy ground states and so the Witten index is equal to zero. The Witten index of the supersymmetric sigma model on a manifold is given by the manifold's Euler characteristic.* p191 (10.124) :\textrm -1)^F e^\sum_(-1)^pb_p=\chi(M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vafa–Witten Theorem
In theoretical physics, the Vafa–Witten theorem, named after Cumrun Vafa and Edward Witten, is a theorem that shows that vector-like global symmetries (those that transform as expected under reflections) such as isospin and baryon number in vector-like gauge theories like quantum chromodynamics cannot be spontaneously broken as long as the theta angle is zero. This theorem can be proved by showing the exponential fall off of the propagator of fermions. See also *F-theory In theoretical physics, F-theory is a branch of string theory developed by Iranian physicist Cumrun Vafa. The new vacua described by F-theory were discovered by Vafa and allowed string theorists to construct new realistic vacua — in the fo ... References * * Gauge theories Theorems in quantum mechanics {{quantum-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gromov–Witten Invariant
In mathematics, specifically in symplectic topology and algebraic geometry, Gromov–Witten (GW) invariants are rational numbers that, in certain situations, count pseudoholomorphic curves meeting prescribed conditions in a given symplectic manifold. The GW invariants may be packaged as a homology or cohomology class in an appropriate space, or as the deformed cup product of quantum cohomology. These invariants have been used to distinguish symplectic manifolds that were previously indistinguishable. They also play a crucial role in closed type IIA string theory. They are named after Mikhail Gromov and Edward Witten. The rigorous mathematical definition of Gromov–Witten invariants is lengthy and difficult, so it is treated separately in the stable map article. This article attempts a more intuitive explanation of what the invariants mean, how they are computed, and why they are important. Definition Consider the following: *''X'': a closed symplectic manifold of dimension ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Weinberg–Witten Theorem
In theoretical physics, the Weinberg–Witten (WW) theorem, proved by Steven Weinberg and Edward Witten, states that massless particles (either composite or elementary) with spin ''j'' > 1/2 cannot carry a Lorentz-covariant current, while massless particles with spin ''j'' > 1 cannot carry a Lorentz-covariant stress-energy. The theorem is usually interpreted to mean that the graviton (''j'' = 2) cannot be a composite particle in a relativistic quantum field theory. Background During the 1980s, preon theories, technicolor and the like were very popular and some people speculated that gravity might be an emergent phenomenon or that gluons might be composite. Weinberg and Witten, on the other hand, developed a no-go theorem that excludes, under very general assumptions, the hypothetical composite and emergent theories. Decades later new theories of emergent gravity are proposed and some high-energy physicists are still using this theorem to try and refute such theories. Becau ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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