A superspace formulation of Abelian antisymmetric tensor gauge theory

TL;DR

This paper develops a superspace formulation for a four-dimensional Abelian antisymmetric tensor gauge theory, simplifying BRS transformations and deriving the Ward-Takahashi identity without the horizontality condition.

Contribution

It introduces a six-dimensional superspace approach that directly realizes BRS transformations as equations of motion, providing a new framework for Abelian tensor gauge theories.

Findings

Superspace formulation reproduces the standard generating functional.

BRS transformations are realized as Euler-Lagrange equations.

WT identity is compactly expressed as a superspace derivative condition.

Abstract

We apply a superspace formulation to the four-dimensional gauge theory of a massless Abelian antisymmetric tensor field of rank 2. The theory is formulated in a six-dimensional superspace using rank-2 tensor, vector and scalar superfields and their associated supersources. It is shown that BRS transformation rules of fields are realized as Euler-Lagrange equations without assuming the so-called horizontality condition and that a generating functional $\bar{W}$ constracted in the superspace reduces to that for the ordinary gauge theory of Abelian rank-2 antisymmetric tensor field. The WT identity for this theory is derived by making use of the superspace formulation and is expressed in a neat and compact form $\partial\bar{W}/\partial\theta=0$.