High Spin Topologically Massive Gravity

TL;DR

This paper introduces a new action for high spin topologically massive gravity with a negative cosmological constant, incorporating gauge fields and Chern-Simons terms, and analyzes fluctuations around AdS3.

Contribution

The paper develops a novel gauge-invariant action for high spin topologically massive gravity and explores its gauge symmetry and fluctuation spectrum.

Findings

Fluctuations satisfy third order differential equations.

Existence of massive traceless and trace modes for each spin.

Relation between gauge field fluctuations and Frondal fields.

Abstract

We propose an action to describe high spin topologically massive gravity with a negative cosmological constant. With the frame-like fields and spin connections being combined into two gauge fields, the action includes two gauge field Chern-Simons actions with different levels, and also a linear term proportional to the difference of the gauge field strengths. Such linear term play the role of imposing the torsion free conditions for high spin fields. We discuss the gauge symmetry of this action and study the fluctuations around the AdS$_3$ vacuum. We show how to relate the the fluctuations of the gauge field to the Frondal fields, using the gauge symmetry. For the gauge group $SL(n,R)\times SL(n,R)$, we find that the fluctuations of all high spin fields up to spin $n$ satisfy third order differential equations, and hence there generically exist massive traceless and trace mode for every spin.