Interpolating gauge-fixing for Yang-Mills-Chern-Simons theory in D=3

TL;DR

This paper introduces an interpolating gauge-fixing scheme for 3D Yang-Mills-Chern-Simons theory, proving its ultraviolet finiteness and vanishing of all beta functions and anomalous dimensions to all orders.

Contribution

It develops a novel gauge-fixing approach that smoothly connects covariant and light-cone gauges, and proves the theory's ultraviolet finiteness using algebraic renormalization.

Findings

Ultraviolet finiteness of the theory is established.

All beta functions and anomalous dimensions vanish to all orders.

The interpolating gauge simplifies the analysis of gauge theories.

Abstract

The Yang-Mills-Chern-Simons theory in three-dimensional Minkowski space-time is studied in a gauge-fixing scheme which interpolates between the covariant gauge and light-cone gauge, the interpolating gauge-fixing. The ultraviolet finiteness of the theory is proved via the Becchi-Rouet-Stora (BRS) algebraic renormalization procedure, which allows us to demonstrate the vanishing of all $\beta$-functions and all anomalous dimensions to all orders in perturbation theory.