Is it Physically Sound to Add a Topologically Massive Term to Three-Dimensional Massive Electromagnetic or Gravitational Models ?

TL;DR

This paper investigates whether adding topologically massive terms to three-dimensional massive electromagnetic and gravitational models preserves unitarity, finding that it does for electromagnetic models but not for gravitational ones, due to fundamental differences.

Contribution

It provides a detailed analysis explaining why topologically massive terms preserve unitarity in electromagnetic models but spoil it in gravitational models.

Findings

Topologically massive electromagnetic models remain unitary.

Topologically massive gravitational models lose unitarity.

The paper explains the fundamental reasons behind these differences.

Abstract

The addition of a topologically massive term to an admittedly non-unitary three-dimensional massive model, be it an electromagnetic system or a gravitational one, does not cure its non-unitarity. What about the enlargement of avowedly unitary massive models by way of a topologically massive term? The electromagnetic models remain unitary after the topological augmentation but, surprisingly enough, the gravitational ones have their unitarity spoiled. Here we analyze these issues and present the explanation why unitary massive gravitational models, unlike unitary massive electromagnetic ones, cannot coexist from the viewpoint of unitarity with topologically massive terms. We also discuss the novel features of the three-term effective field models that are gauge-invariant.