Dimensional reduction in supersymmetric field theories

Abstract

A class of quantum field theories invariant with respect to the action of an odd vector field Q on a source supermanifold $\Sigma$ is considered. We suppose that Q satisfies the conditions under which an integral of any Q-invariant function over $\Sigma$ localizes to the zero locus of Q. The Q-invariant sector of a field theory from the class above is shown then to be equivalent to the quantum field theory defined on zero locus of the vector field Q.

11 pages, Latex ,no figures

References in corpus (2)

• Semiclassical approximation in Batalin-Vilkovisky formalism
• Equivariant Localization of Path Integrals

Cited by in corpus (1)

• Random Field Ising Model and Parisi-Sourlas Supersymmetry. Part II. Renormalization Group