More about the renormalization properties of topological Yang-Mills theories

TL;DR

This paper investigates the renormalization properties of topological Yang-Mills theories in generalized gauges, demonstrating their renormalizability and discussing ambiguities in renormalization factors.

Contribution

It extends the analysis of renormalizability to new classes of gauges depending on parameters, revealing the theory's robustness and exploring renormalization ambiguities.

Findings

The theory remains renormalizable in generalized gauges.

The (anti-)self-dual Landau gauge is a special case within these classes.

Ambiguities in renormalization factors are identified and discussed.

Abstract

Quantum properties of topological Yang-Mills theory in (anti-)self-dual Landau gauge were recently investigated by the authors. We extend the analysis of renormalizability for two generalized classes of gauges; each of them depending on one gauge parameter. The (anti-)self-dual Landau gauge is recovered at the vanishing of each gauge parameter. The theory shows itself to be renormalizable in these classes of gauges. Moreover, we discuss the ambiguity on the choice of the renormalization factors (which is not present in usual Yang-Mills theories) and argue a possible origin of such ambiguity.