Gauge (In)variance, Mass and Parity in D=3 Revisited

Summary

Abstract

We analyze the degree of equivalence between abelian topologically massive, gauge-invariant, vector or tensor parity doublets and their explicitly massive, non-gauge, counterparts. We establish equivalence of field equations by exploiting a generalized Stueckelberg invariance of the gauge systems. Although the respective excitation spectra and induced source-source interactions are essentially identical, there are also differences, most dramatic being those between the Einstein limits of the interactions in the tensor case: the doublets avoid the discontinuity (well-known from D=4) exhibited by Pauli—Fierz theory.

It is a pleasure to dedicate this work to Dieter Brill on the occasion of his 60th birthday. I have learned much from him over the years, not least during our old collaborations on general relativity. I hope he will be entertained by these considerations of related theories in another dimension.

Introduction

Perhaps the most paradoxical feature of topologically massive (TM) theories [1, 2] is that their gauge invariance coexists with the finite mass and single helicity, parity violating, character of their excitations. This phenomenon, common to vector (TME) and tensor (TMG) models, is special to 2+1 dimensions because in higher (odd) dimensions the operative Chern—Simons (CS) terms are of at least cubic order in these fields and so do not affect their kinematics; only higher rank tensors could acquire a topological mass there.