Massive, Topologically Massive, Models

TL;DR

This paper investigates three-term massive gauge models in three dimensions, revealing their physical inconsistencies and exploring their gauge invariance properties, contrasting with vector models.

Contribution

It analyzes the physical viability of combined Proca/Pauli-Fierz and Chern-Simons mass terms in three-dimensional gauge theories and uncovers issues like complex masses and ghosts.

Findings

Tensor models with these mass terms are physically unacceptable.

Complex masses arise when the Einstein term sign is 'wrong'.

Ghost problems occur in certain parameter regimes.

Abstract

In three dimensions, there are two distinct mass-generating mechanisms for gauge fields: adding the usual Proca/Pauli-Fierz, or the more esoteric Chern-Simons (CS), terms. Here we analyze the three-term models where both types are present, and their various limits. Surprisingly, in the tensor case, these seemingly innocuous systems are physically unacceptable. If the sign of the Einstein term is ``wrong'' as is in fact required in the CS case, then the excitation masses are always complex; with the usual sign, there is a (known) region of the two mass parameters where reality is restored, but instead we show that a ghost problem arises, while, for the ``pure mass'' two-term system without an Einstein action, complex masses are unavoidable. This contrasts with the smooth behavior of the corresponding vector models. Separately, we show that the ``partial masslessness'' exhibited by (plain) massive spin-2 models in de Sitter backgrounds is formally shared by the three-term system: it also enjoys a reduced local gauge invariance when this mass parameter is tuned to the cosmological constant.