Spin-3 Topological Massive Gravity

TL;DR

The paper extends topologically massive gravity in AdS$_3$ to include a spin-3 field by formulating a spin-3 TMG action within a CS-like framework based on $SL(3,\mathbb{R})$. It shows that, away from the chiral point, a local massive spin-3 mode exists with conformal weights $(\mu l+2,\mu l-1)$, which degenerates with the left-moving mode at ${\mu l=1}$, rendering both effectively pure gauge. At the chiral point, the theory has only right-moving boundary degrees of freedom, consistent with a holomorphic $W_3$-algebra in the dual CFT with central charge $c_R=3l/G$. The results support a spin-3 chiral gravity picture holographically dual to a 2D chiral CFT and point toward a holomorphic Chern-Simons description with $SL(3,\mathbb{R})$ in the chiral limit.

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 $c_R=3l/G$.