Equivariant Localization for Supersymmetric Quantum Mechanics

TL;DR

This paper develops a novel equivariant localization method for supersymmetric quantum mechanics, revealing how the partition function concentrates on instantons and extending the symmetry structure to facilitate localization.

Contribution

It introduces a new construction of equivariant cohomology for SUSY quantum mechanics, explicitly revealing a hidden bosonic symmetry and extending supersymmetry.

Findings

Partition function localizes on instantons.

New equivariant complex with Cartan differential constructed.

Extended symmetry structure enables localization.

Abstract

We apply equivariant localization to supersymmetric quantum mechanics and show that the partition function localizes on the instantons of the theory. Our construction of equivariant cohomology for SUSY quantum mechanics is different than the ones that already exist in the literature. A hidden bosonic symmetry is made explicit and the supersymmetry is extended. New bosonic symmetry is the square of the new fermionic symmetry. The D term is now the parameter of the bosonic symmetry. This construction provides us with an equivariant complex together with a Cartan differential and makes the use of localization principle possible.