A Vector Supersymmetry in Noncommutative U(1) Gauge Theory with the Slavnov Term

TL;DR

This paper demonstrates that noncommutative U(1) gauge theory with the Slavnov term exhibits a vector supersymmetry, which explains its finiteness and independence from certain loop corrections, akin to the 2D BF model.

Contribution

It reveals a vector supersymmetry in the noncommutative U(1) gauge theory with the Slavnov term, providing insight into its finiteness and loop correction independence.

Findings

The theory exhibits a linear vector supersymmetry.

Loop corrections are independent of the $ ext{lambda} AA$-vertex.

The model is finite under the specified gauge-fixing.

Abstract

We consider noncommutative U(1) gauge theory with the additional term, involving a scalar field lambda, introduced by Slavnov in order to cure the infrared problem. we show that this theory, with an appropriate space-like axial gauge-fixing, wxhibits a linear vector supersymmetry similar to the one present in the 2-dimensional BF model. This vector supersymmetry implies that all loop corrections are independent of the $\lambda AA$-vertex and thereby explains why Slavnov found a finite model for the same gauge-fixing.