Spin-3 Topological Massive Gravity

TL;DR

This paper explores the properties of spin-3 topological massive gravity at the chiral point, revealing a simplified boundary degree of freedom structure and proposing a holographic dual involving a 2D chiral CFT with $W_3$ symmetry.

Contribution

It introduces an action for high spin fields coupled to TMG and analyzes the boundary modes, especially at the chiral point, proposing a holographic dual with $W_3$ algebra.

Findings

Extra massive mode exists in spin-3 fluctuations.

At the chiral point, the mode becomes massless and degenerates.

Boundary degrees of freedom reduce to right-moving graviton and spin-3 field.

Abstract

In this paper, we study the spin-3 topological massive gravity(TMG), paying special attention to its properties at the chiral point. We propose an action describing the high spin fields coupled to TMG. We discuss the spin-3 fluctuations around the AdS$_3$ vacuum and find that there is an extra local massive mode, besides the left-moving and right-moving boundary massless modes. At the chiral point, such extra mode becomes massless and degenerates with the left-moving mode. We show that at the chiral point the only degrees of freedom in the theory are the boundary right-moving graviton and spin-3 field. We conjecture that spin-3 chiral gravity with Brown-Henneaux boundary condition is holographically dual to 2D chiral CFT with classical $W_3$ algebra and central charge $c_R=3l/G$.