Search results
Results from the WOW.Com Content Network
Sergei Novikov generalized this construction to a homology theory associated to a closed one-form on a manifold. Morse homology is a special case for the one-form df. A special case of Novikov's theory is circle-valued Morse theory, which Michael Hutchings and Yi-Jen Lee have connected to Reidemeister torsion and Seiberg–Witten theory.
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.
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 ...
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 ...
The standard paradigm for incorporating supersymmetry into a realistic theory is to have the underlying dynamics of the theory be supersymmetric, but the ground state of the theory does not respect the symmetry and supersymmetry is broken spontaneously. The supersymmetry break can not be done permanently by the particles of the MSSM as they ...
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.
In theoretical physics, the Hořava–Witten theory argues that the cancellation of anomalies guarantees that a supersymmetric gauge theory with the E8 gauge group propagates on a type of domain wall. This domain wall, a Hořava–Witten domain wall, behaves as a boundary of the eleven-dimensional spacetime in M-theory.