Non-Commutative U(1) Gauge Theory on R**4 with Oscillator Term and BRST Symmetry

TL;DR

This paper develops a non-commutative U(1) gauge theory incorporating an oscillator term within a BRST symmetric framework, aiming to establish a renormalizable model inspired by similar scalar theories.

Contribution

It introduces a novel non-commutative gauge theory with an oscillator term and BRST symmetry, providing a promising candidate for renormalizability.

Findings

Propagators are given by the Mehler kernel.

The bilinear action is invariant under Langmann-Szabo duality.

The model is a promising candidate for renormalizability.

Abstract

Inspired by the renormalizability of the non-commutative Phi^4 model with added oscillator term, we formulate a non-commutative gauge theory, where the oscillator enters as a gauge fixing term in a BRST invariant manner. All propagators turn out to be essentially given by the Mehler kernel and the bilinear part of the action is invariant under the Langmann-Szabo duality. The model is a promising candidate for a renormalizable non-commutative U(1) gauge theory.