Superlocalization formulas and supersymmetric Yang-Mills theories

TL;DR

This paper develops superlocalization formulas using supermanifold techniques to analyze supersymmetric Yang-Mills theories, enabling computation of partition functions across various supercharges and dimensions.

Contribution

It generalizes localization formulas to supersymmetric theories via supermanifold methods, broadening their applicability to topological field theories.

Findings

Derived superlocalization formulas applicable to supersymmetric Yang-Mills theories.

Computed reduced partition functions for topological super Yang-Mills with different supercharges.

Established the generality of superlocalization in various dimensions.

Abstract

By using supermanifold techniques we prove a generalization of the localization formula in equivariant cohomology which is suitable for studying supersymmetric Yang-Mills theories in terms of ADHM data. With these techniques one can compute the reduced partition functions of topological super Yang-Mills theory with 4, 8 or 16 supercharges. More generally, the superlocalization formula can be applied to any topological field theory in any number of dimensions.