Covariant quantization of N=1/2 SYM theories and supergauge invariance

TL;DR

This paper develops a gauge-independent superspace approach to quantize N=1/2 super Yang--Mills theories, demonstrating that the one-loop effective action remains gauge invariant despite divergences.

Contribution

It introduces a manifestly gauge-invariant superspace method for NAC SYM theories using a generalized background field and momentum supergraph techniques.

Findings

One-loop effective action is gauge invariant.

Divergent contributions do not break supergauge invariance.

Method enables gauge-independent analysis of NAC supersymmetric theories.

Abstract

So far, quantum properties of N=1/2 nonanticommutative (NAC) super Yang--Mills theories have been investigated in the WZ gauge. The gauge independence of the results requires assuming that at the quantum level supergauge invariance is not broken by nonanticommutative geometry. In this paper we use an alternative approach which allows studying these theories in a manifestly gauge independent superspace setup. This is accomplished by generalizing the background field method to the NAC case, by moving to a momentum superspace where star products are treated as exponential factors and by developing momentum supergraph techniques. We compute the one--loop gauge effective action for NAC U(N) gauge theories with matter in the adjoint representation. Despite the appearance of divergent contributions which break (super)gauge invariance, we prove that the effective action at this order is indeed invariant.