Towards metric-like higher-spin gauge theories in three dimensions

TL;DR

This paper develops a metric-like formulation for higher-spin gauge theories in three dimensions, coupling spin-3 fields to gravity, and applies it to compute black hole entropy corrections.

Contribution

It introduces a second order metric-like action for spin-3 fields coupled to 3D gravity and relates it to Chern-Simons theory, enabling entropy calculations.

Findings

Derived quadratic order action for spin-3 coupling

Connected metric-like and frame-like formulations

Computed higher-spin black hole entropy corrections

Abstract

We consider the coupling of a symmetric spin-3 gauge field to three-dimensional gravity in a second order metric-like formulation. The action that corresponds to an SL(3,R) x SL(3,R) Chern-Simons theory in the frame-like formulation is identified to quadratic order in the spin-3 field. We apply our result to compute corrections to the area law for higher-spin black holes using Wald's entropy formula.