A ``Gaussian'' Approach to Computing Supersymmetric Effective Actions

TL;DR

This paper introduces a Gaussian-based method for calculating supersymmetric effective actions by extending heat kernel techniques to superspace, enabling efficient integration of massive supermultiplets in supersymmetric Yang-Mills backgrounds.

Contribution

It develops a novel Gaussian integral approach for computing supersymmetric effective actions within superspace frameworks.

Findings

Successfully computes low energy effective actions in supersymmetric theories.

Extends heat kernel methods to superspace for supersymmetric models.

Provides a practical technique for integrating out massive supermultiplets.

Abstract

For nonsupersymmetric theories, the one-loop effective action can be computed via zeta function regularization in terms of the functional trace of the heat kernel associated with the operator which appears in the quadratic part of the action. A method is developed for computing this functional trace by exploiting its similarity to a Gaussian integral. The procedure is extended to superspace, where it is used to compute the low energy effective action obtained by integrating out massive scalar supermultiplets in the presence of a supersymmetric Yang-Mills background.