On the regularization scheme and gauge choice ambiguities in topologically massive gauge theories

TL;DR

This paper demonstrates a regularization scheme for (2+1)-dimensional topologically massive gauge theories that preserves symmetries and clarifies gauge choice ambiguities, especially in non-covariant gauges.

Contribution

It introduces a Pauli-Villars regularization method using auxiliary fermions with opposite sign masses that maintains symmetries and resolves gauge ambiguities.

Findings

Regularization with auxiliary fermions aligns different schemes.

Ambiguities in covariant gauges are clarified and mitigated in softer gauges.

Trace of gauge symmetry breaking disappears after regularization removal.

Abstract

It is demonstrated that in the (2+1)-dimensional topologically massive gauge theories an agreement of the Pauli-Villars regularization scheme with the other schemes can be achieved by employing pairs of auxiliary fermions with the opposite sign masses. This approach does not introduce additional violation of discrete (P and T) symmetries. Although it breaks the local gauge symmetry only in the regulator fields' sector, its trace disappears completely after removing the regularization as a result of superrenormalizability of the model. It is shown also that analogous extension of the Pauli-Villars regularization in the vector particle sector can be used to agree the arbitrary covariant gauge results with the Landau ones. The source of ambiguities in the covariant gauges is studied in detail. It is demonstrated that in gauges that are softer in the infrared region (e.g. Coulomb or axial) nonphysical ambiguities inherent to the covariant gauges do not arise.