A perturbative re-analysis of N=4 supersymmetric Yang--Mills theory

TL;DR

This paper reanalyzes the finiteness and divergence properties of N=4 supersymmetric Yang-Mills theory using component and superfield methods, revealing subtleties in gauge dependence and proposing a mass-deformed model as a potential regularization scheme.

Contribution

It provides a detailed perturbative analysis of divergences in N=4 SYM, highlighting gauge-dependent infrared issues and introducing a mass deformation as a supersymmetry-preserving regularization approach.

Findings

Wess-Zumino gauge introduces UV divergences in propagators.

Infrared divergences occur in N=1 superfield formulation outside Fermi-Feynman gauge.

Mass deformation removes UV divergences in two-point functions.

Abstract

The finiteness properties of the N=4 supersymmetric Yang-Mills theory are reanalyzed both in the component formulation and using N=1 superfields, in order to discuss some subtleties that emerge in the computation of gauge dependent quantities. The one-loop corrections to various Green functions of elementary fields are calculated. In the component formulation it is shown that the choice of the Wess-Zumino gauge, that is standard in supersymmetric gauge theories, introduces ultraviolet divergences in the propagators at the one-loop level. Such divergences are exactly cancelled when the contributions of the fields that are put to zero in the Wess-Zumino gauge are taken into account. In the description in terms of N=1 superfields infrared divergences are found for every choice of gauge different from the supersymmetric generalization of the Fermi-Feynman gauge. Two-, three- and four-point functions of N=1 superfields are computed and some general features of the infrared problem are discussed. We also examine the effect of the introduction of mass terms for the (anti) chiral superfields in the theory, which break supersymmetry from N=4 to N=1. It is shown that in the mass deformed model no ultraviolet divergences appear in two-point functions. It argued that this result can be generalized to n-point functions, supporting the proposal of a possible of use of this modified model as a supersymmetry-preserving regularization scheme for N=1 theories.