Divergences in Non-Commutative Gauge Theories with the Slavnov Term

TL;DR

This paper investigates the divergence structure of non-commutative gauge theories with the Slavnov extension, revealing that certain IR divergences are gauge-independent and identifying new UV divergences consistent with gauge invariance.

Contribution

It provides a detailed one-loop analysis of divergences in non-commutative gauge theories with Slavnov extension, highlighting gauge independence of IR divergences and introducing new UV divergences.

Findings

Quadratic IR divergence is gauge-independent.

New UV divergences are compatible with gauge invariance.

Analysis includes models with fermions and scalar fields.

Abstract

The divergence structure of non-commutative gauge field theories (NCGFT) with a Slavnov extension is examined at one-loop level with main focus on the gauge boson self-energy. Using an interpolating gauge we show that even with this extension the quadratic IR divergence of the gauge boson self-energy is independent from a covariant gauge fixing as well as from an axial gauge. The proposal of Slavnov is based on the fact that the photon propagator shows a new transversality condition with respect to the IR dangerous terms. This novel transversality is implemented with the help of a new dynamical multiplier field. However, one expects that in physical observables such contributions disappear. A further new feature is the existence of new UV divergences compatible with the gauge invariance (BRST symmetry). We then examine two explicit models with couplings to fermions and scalar fields.