Construction of the effective action in nonanticommutative supersymmetric field theories

TL;DR

This paper develops a gauge-invariant method to compute the one-loop effective action in nonanticommutative supersymmetric gauge theories formulated in ${\cal N}=1/2$ superspace, enabling exact calculations of low-energy effects.

Contribution

It introduces a novel, unambiguous construction of the one-loop effective action in ${\cal N}=1/2$ supersymmetric gauge theories using covariant techniques.

Findings

Successfully defines the effective action for matter and vector multiplets in ${\cal N}=1/2$ superspace.

Calculates the low-energy one-loop effective action for matter and SU(2) SYM theory.

Provides a framework for exact low-energy effective action computations in nonanticommutative supersymmetric theories.

Abstract

We develop a general gauge invariant construction of the one-loop effective action for supersymmetric gauge field theories formulated in ${\cal N}=1/2$ superspace. Using manifestly covariant techniques (the background superfield method and proper-time representations) adopted to the ${\cal N}=1/2$ superspace we show how to define unambiguously the effective action of a matter multiplet (in fundamental and adjoint representations) and the vector multiplet coupled to a background ${\cal N}=1/2$ gauge superfield. As an application of this construction we exactly calculate the low-energy one-loop effective action of matter multiplet and SU(2) SYM theory on the Abelian background.