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3D Mirror Symmetry
In theoretical physics, 3D mirror symmetry is a version of mirror symmetry in 3-dimensional gauge theories with N=4 supersymmetry, or 8 supercharges. It was first proposed by Kenneth Intriligator and Nathan Seiberg, in their 1996 paper "Mirror symmetry in three-dimensional gauge theories", as a relation between pairs of 3-dimensional gauge theories, such that the Coulomb branch of the moduli space of one is the Higgs branch of the moduli space of the other. It was demonstrated using D-brane cartoons by Amihay Hanany and Edward Witten 4 months later, where they found that it is a consequence of S-duality in type IIB string theory. Four months later 3D mirror symmetry was extended to N=2 gauge theories resulting from supersymmetry breaking in N=4 theories. Here it was given a physical interpretation in terms of vortices. In 3-dimensional gauge theories, vortices are particles. BPS vortices, which are those vortices that preserve some supersymmetry, have masses which are given b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mirror Symmetry (string Theory)
In algebraic geometry and theoretical physics, mirror symmetry is a relationship between geometric objects called Calabi–Yau manifolds. The term refers to a situation where two Calabi–Yau manifolds look very different geometrically but are nevertheless equivalent when employed as extra dimensions of string theory. Early cases of mirror symmetry were discovered by physicists. Mathematicians became interested in this relationship around 1990 when Philip Candelas, Xenia de la Ossa, Paul Green, and Linda Parkes showed that it could be used as a tool in enumerative geometry, a branch of mathematics concerned with counting the number of solutions to geometric questions. Candelas and his collaborators showed that mirror symmetry could be used to count rational curves on a Calabi–Yau manifold, thus solving a longstanding problem. Although the original approach to mirror symmetry was based on physical ideas that were not understood in a mathematically precise way, some of its mathem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
S-duality
In theoretical physics, S-duality (short for strong–weak duality, or Sen duality) is an equivalence of two physical theories, which may be either quantum field theories or string theories. S-duality is useful for doing calculations in theoretical physics because it relates a theory in which calculations are difficult to a theory in which they are easier. In quantum field theory, S-duality generalizes a well established fact from classical electrodynamics, namely the invariance of Maxwell's equations under the interchange of electric and magnetic fields. One of the earliest known examples of S-duality in quantum field theory is Montonen–Olive duality which relates two versions of a quantum field theory called ''N'' = 4 supersymmetric Yang–Mills theory. Recent work of Anton Kapustin and Edward Witten suggests that Montonen–Olive duality is closely related to a research program in mathematics called the geometric Langlands program. Another realization of S-duality in quan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Holomorph (mathematics)
In mathematics, especially in the area of algebra known as group theory, the holomorph of a group is a group that simultaneously contains (copies of) the group and its automorphism group. The holomorph provides interesting examples of groups, and allows one to treat group elements and group automorphisms in a uniform context. In group theory, for a group G, the holomorph of G denoted \operatorname(G) can be described as a semidirect product or as a permutation group. Hol(''G'') as a semidirect product If \operatorname(G) is the automorphism group of G then :\operatorname(G)=G\rtimes \operatorname(G) where the multiplication is given by :(g,\alpha)(h,\beta)=(g\alpha(h),\alpha\beta). q. 1 Typically, a semidirect product is given in the form G\rtimes_A where G and A are groups and \phi:A\rightarrow \operatorname(G) is a homomorphism and where the multiplication of elements in the semidirect product is given as :(g,a)(h,b)=(g\phi(a)(h),ab) which is well defined, since \phi(a)\in \opera ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
't Hooft–Polyakov Monopole
__NOTOC__ In theoretical physics, the t Hooft–Polyakov monopole is a topological soliton similar to the Dirac monopole but without the Dirac string. It arises in the case of a Yang–Mills theory with a gauge group G, coupled to a Higgs field which spontaneously breaks it down to a smaller group H via the Higgs mechanism. It was first found independently by Gerard 't Hooft and Alexander Polyakov. Unlike the Dirac monopole, the 't Hooft–Polyakov monopole is a smooth solution with a finite total energy. The solution is localized around r=0. Very far from the origin, the gauge group G is broken to H, and the 't Hooft–Polyakov monopole reduces to the Dirac monopole. However, at the origin itself, the G gauge symmetry is unbroken and the solution is non-singular also near the origin. The Higgs field :H_i \qquad (i=1,2,3) \, is proportional to :x_i f(, x, ) \, where the adjoint indices are identified with the three-dimensional spatial indices. The gauge field at infinity is suc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Instanton
An instanton (or pseudoparticle) is a notion appearing in theoretical and mathematical physics. An instanton is a classical solution to equations of motion with a finite, non-zero action, either in quantum mechanics or in quantum field theory. More precisely, it is a solution to the equations of motion of the classical field theory on a Euclidean spacetime. In such quantum theories, solutions to the equations of motion may be thought of as critical points of the action. The critical points of the action may be local maxima of the action, local minima, or saddle points. Instantons are important in quantum field theory because: * they appear in the path integral as the leading quantum corrections to the classical behavior of a system, and * they can be used to study the tunneling behavior in various systems such as a Yang–Mills theory. Relevant to dynamics, families of instantons permit that instantons, i.e. different critical points of the equation of motion, be related to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Squarks
In supersymmetric extension to the Standard Model (SM) of physics, a sfermion is a hypothetical spin-0 superpartner particle (sparticle) of its associated fermion. Each particle has a superpartner with spin that differs by . Fermions in the SM have spin- and, therefore, sfermions have spin 0. The name 'sfermion' was formed by the general rule of prefixing an 's' to the name of its superpartner, denoting that it is a scalar particle with spin 0. For instance, the electron's superpartner is the selectron and the top quark's superpartner is the stop squark. One corollary from supersymmetry is that sparticles have the same gauge numbers as their SM partners. This means that sparticle–particle pairs have the same color charge, weak isospin charge, and hypercharge (and consequently electric charge). Unbroken supersymmetry also implies that sparticle–particle pairs have the same mass. This is evidently not the case, since these sparticles would have already been detecte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Supersymmetry Breaking
In particle physics, supersymmetry breaking is the process to obtain a seemingly non-supersymmetric physics from a supersymmetric theory which is a necessary step to reconcile supersymmetry with actual experiments. It is an example of spontaneous symmetry breaking. In supergravity, this results in a slightly modified counterpart of the Higgs mechanism where the gravitinos become massive. Supersymmetry breaking occurs at supersymmetry breaking scale. The superpartners, whose mass would otherwise be equal to the mass of the regular particles in the absence of the SUSY breaking, become much heavier. In the domain of applicability of stochastic differential equations including, e.g, classical physics, spontaneous supersymmetry breaking encompasses such nonlinear dynamical phenomena as chaos theory, chaos, turbulence, pink noise, etc. Supersymmetry breaking scale In particle physics, supersymmetry breaking scale is the energy scale where supersymmetry breaking takes place. If sup ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 gra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Supersymmetry
In a supersymmetric theory the equations for force and the equations for matter are identical. In theoretical and mathematical physics, any theory with this property has the principle of supersymmetry (SUSY). Dozens of supersymmetric theories exist. Supersymmetry is a spacetime symmetry between two basic classes of particles: bosons, which have an integer-valued spin and follow Bose–Einstein statistics, and fermions, which have a half-integer-valued spin and follow Fermi–Dirac statistics. In supersymmetry, each particle from one class would have an associated particle in the other, known as its superpartner, the spin of which differs by a half-integer. For example, if the electron exists in a supersymmetric theory, then there would be a particle called a ''"selectron"'' (superpartner electron), a bosonic partner of the electron. In the simplest supersymmetry theories, with perfectly " unbroken" supersymmetry, each pair of superpartners would share the same mass and intern ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Amihay Hanany
Amihai ( he, עַמִּיחַי) is an Israeli settlement organized as a communal settlement in the Shilo settlement bloc in the West Bank. In it had a population of . The international community considers all Israeli settlements in the West Bank illegal under international law, which the Israeli government disputes. There is a plan to expand Amihai both west and east, and to include the outpost of Adei Ad (currently illegal even under Israeli law) in its jurisdiction, thereby legalizing the outpost. This is a highly controversial plan, which according to both critics and advocates, will result in the effective severance of West Bank's territorial contiguity, specifically between Central West Bank (Ramallah and Jerusalem) and Northern West Bank (Nablus, Jenin, etc.). This would have the effect of undermining the prospects of the realization of the Two-state solution.“Settlement Report: November 15, 2018.” Foundation for Middle East Peace, November 15, 2018https://fmep.org/ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
D-brane
In string theory, D-branes, short for ''Dirichlet membrane'', are a class of extended objects upon which open strings can end with Dirichlet boundary conditions, after which they are named. D-branes were discovered by Jin Dai, Leigh, and Polchinski, and independently by Hořava, in 1989. In 1995, Polchinski identified D-branes with black p-brane solutions of supergravity, a discovery that triggered the Second Superstring Revolution and led to both holographic and M-theory dualities. D-branes are typically classified by their spatial dimension, which is indicated by a number written after the ''D.'' A D0-brane is a single point, a D1-brane is a line (sometimes called a "D-string"), a D2-brane is a plane, and a D25-brane fills the highest-dimensional space considered in bosonic string theory. There are also instantonic D(–1)-branes, which are localized in both space and time. Theoretical background The equations of motion of string theory require that the endpoints of an o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
