Supersymmetry and localization

TL;DR

This paper explores how certain odd symmetries in integrals over supermanifolds can cause localization, often making stationary phase approximations exact, which simplifies complex calculations in supersymmetric theories.

Contribution

It establishes conditions linking odd symmetries to localization and exact stationary phase approximations in supermanifold integrals.

Findings

Conditions for symmetry-induced localization are identified.

Stationary phase approximation can be exact under these conditions.

Implications for supersymmetric integral calculations are discussed.

Abstract

We study conditions under which an odd symmetry of the integrand leads to localization of the corresponding integral over a (super)manifold. We also show that in many cases these conditions guarantee exactness of the stationary phase approximation of such integrals.