Extended BRST cohomology, consistent deformations and anomalies of four-dimensional supersymmetric gauge theories

TL;DR

This paper computes the local cohomology of an extended BRST differential in four-dimensional N=1 supersymmetric gauge theories, classifies consistent deformations, and identifies potential anomalies, advancing understanding of supersymmetric gauge invariance and anomalies.

Contribution

It explicitly determines all first-order supersymmetric and Poincare invariant deformations and anomalies in four-dimensional N=1 supersymmetric gauge theories, including cases with linear multiplets.

Findings

All deformations can be constructed from superspace integrals in certain cases.

Candidate anomalies are related to supersymmetric generalizations of chiral anomalies.

Additional deformations and anomalies are identified in the general case, relevant to free theories.

Abstract

The local cohomology of an extended BRST differential which includes global N=1 supersymmetry and Poincare transformations is completely and explicitly computed in four-dimensional supersymmetric gauge theories with super-Yang-Mills multiplets, chiral matter multiplets and linear multiplets containing 2-form gauge potentials. In particular we determine to first order all N=1 supersymmetric and Poincare invariant consistent deformations of these theories that preserve the N=1 supersymmetry algebra on-shell modulo gauge transformations, and all Poincare invariant candidate gauge and supersymmetry anomalies. When the Yang-Mills gauge group is semisimple and no linear multiplets are present, we find that all such deformations can be constructed from standard superspace integrals and preserve the supersymmetry transformations in a formulation with auxiliary fields, and the candidate anomalies are exhausted by supersymmetric generalizations of the well-known chiral anomalies. In the general case there are additional deformations and candidate anomalies which are relevant especially to the deformation of free theories and the general classification of interaction terms in supersymmetric field theories.