On the Background Field Method Beyond One Loop: A manifestly covariant derivative expansion in super Yang-Mills theories

TL;DR

This paper develops a covariant derivative expansion for super Yang-Mills theories to facilitate multi-loop calculations of the effective action using the background field method, advancing theoretical tools in supersymmetric quantum field theory.

Contribution

It introduces a new scheme for evaluating multi-loop contributions in super Yang-Mills theories through a covariant derivative expansion of superspace heat kernels.

Findings

Provides a detailed analysis of parallel displacement propagators in N-extended superspace.

Establishes a framework for explicit multi-loop calculations in super Yang-Mills theories.

Enhances the computational methods for low-energy effective actions in supersymmetric models.

Abstract

There are currently many string inspired conjectures about the structure of the low-energy effective action for super Yang-Mills theories which require explicit multi-loop calculations. In this paper, we develop a manifestly covariant derivative expansion of superspace heat kernels and present a scheme to evaluate multi-loop contributions to the effective action in the framework of the background field method. The crucial ingredient of the construction is a detailed analysis of the properties of the parallel displacement propagators associated with Yang-Mills supermultiples in N-extended superspace.