Background field formalism and construction of effective action for N=2, d=3 supersymmetric gauge theories

TL;DR

This paper reviews the background field method and heat kernel techniques for calculating the low-energy effective actions in three-dimensional N=2 supersymmetric gauge theories, providing exact heat kernel expressions for constant backgrounds.

Contribution

It introduces superfield proper time techniques and applies them to evaluate effective actions in various N=2, N=4, and N=8 supersymmetric models, advancing computational methods in supersymmetric gauge theories.

Findings

Derived exact heat kernel expressions for constant backgrounds.

Applied techniques to evaluate low-energy effective actions.

Extended methods to N=4 and N=8 supersymmetric theories.

Abstract

We review the background field method for three-dimensional Yang-Mills and Chern-Simons models in N=2 superspace. Superfield proper time (heat kernel) techniques are developed and exact expressions of heat kernels for constant backgrounds are presented. The background field method and heat kernel techniques are applied for evaluating the low-energy effective actions in N=2 supersymmetric Yang-Mills and Chern-Simons models as well as in N=4 and N=8 SYM theories.