High Spin Topologically Massive Gravity

TL;DR

The paper develops a higher-spin extension of topologically massive gravity in AdS3 by proposing a first-order action in which torsion-free constraints for all higher-spin fields are imposed through a single beta-term. It analyzes the gauge structure and shows that linearized gauge symmetry re-emerges around the AdS3 vacuum, enabling a clean decomposition of fluctuations into Fronsdal-type fields. The linearized equations for spins up to n are third-order, yielding massive modes for each spin and reproducing known spin-s TMG results. The framework is versatile, with potential generalizations to other gauge groups and vacua, and offers a path toward exploring holographic duals and high-spin hair in non-Einstein backgrounds.

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.