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Given a Lie subgroup , the / gauged WZW model (or coset model) is a nonlinear sigma model whose target space is the quotient / for the adjoint action of on . This gauged WZW model is a conformal field theory, whose symmetry algebra is a quotient of the two affine Lie algebras of the G {\displaystyle G} and H {\displaystyle H} WZW models, and ...
A third area mentioned in Atiyah's address is Witten's work relating supersymmetry and Morse theory, [29] a branch of mathematics that studies the topology of manifolds using the concept of a differentiable function.
In quantum field theory, supersymmetry is motivated by solutions to several theoretical problems, for generally providing many desirable mathematical properties, and for ensuring sensible behavior at high energies. Supersymmetric quantum field theory is often much easier to analyze, as many more problems become mathematically tractable.
Before Morse, Arthur Cayley and James Clerk Maxwell had developed some of the ideas of Morse theory in the context of topography. Morse originally applied his theory to geodesics (critical points of the energy functional on the space of paths). These techniques were used in Raoul Bott's proof of his periodicity theorem. The analogue of Morse ...
M-theory is a theory in physics that unifies all consistent versions of superstring theory. Edward Witten first conjectured the existence of such a theory at a string theory conference at the University of Southern California in 1995. Witten's announcement initiated a flurry of research activity known as the second superstring revolution. Prior ...
Supersymmetric theory of stochastic dynamics (STS) is a multidisciplinary approach to stochastic dynamics on the intersection of dynamical systems theory, statistical physics, stochastic differential equations (SDE), topological field theories, and the theory of pseudo-Hermitian operators. The theory can be viewed as a generalization of the ...
In theoretical physics, supergravity (supergravity theory; SUGRA for short) is a modern field theory that combines the principles of supersymmetry and general relativity; this is in contrast to non-gravitational supersymmetric theories such as the Minimal Supersymmetric Standard Model. Supergravity is the gauge theory of local
The dual theory has different field content, with two = chiral superfields , ~, and gauge field the dual photon , with a potential that gives equations of motion which are Witten's monopole equations, also known as the Seiberg–Witten equations at the critical points = where the monopoles become massless.