On Topologically Massive Spin-2 Gauge Theories beyond Three Dimensions

TL;DR

This paper explores extending 3D topologically massive gravity to higher odd dimensions, constructing massive spin-2 gauge theories using novel representations, and analyzing their degrees of freedom and unitarity.

Contribution

It introduces a new class of topologically massive spin-2 gauge theories in dimensions 4k-1 using non-standard Young tableau representations, expanding the understanding beyond three dimensions.

Findings

A free topologically massive gauge theory in 7D with 35 degrees of freedom.

The model describes unitarily the massive spin-2 particles.

Discussion on the interaction aspects compared to 3D case.

Abstract

We investigate in which sense, at the linearized level, one can extend the 3D topologically massive gravity theory beyond three dimensions. We show that, for each k=1,2,3... a free topologically massive gauge theory in 4k-1 dimensions can be defined describing a massive "spin-2" particle provided one uses a non-standard representation of the massive "spin-2" state which makes use of a two-column Young tableau where each column is of height 2k-1. We work out the case of k=2, i.e. 7D, and show, by canonical analysis, that the model describes, unitarily, 35 massive "spin-2" degrees of freedom. The issue of interactions is discussed and compared with the three-dimensional situation.