Topologically Massive Higher Spin Gravity

TL;DR

Topologically Massive Gravity is extended to spin-3 in AdS3 by adding a parity-violating Chern-Simons term. The linearised equations factor into three commuting operators, revealing massive, left, and right branches, with an additional trace sector that cannot be gauged away. At the chiral point $\mu\ell=1$, logarithmic modes appear; the log-partner of the traceless mode carries negative energy, indicating bulk instability, while trace-log modes show positive energy, complicating dual interpretations. The authors discuss asymptotic W3 symmetries and propose a contracted Virasoro structure, suggesting a higher-spin LCFT dual; they outline future work including boundary conditions and one-loop partition functions.

Abstract

We look at the generalisation of topologically massive gravity (TMG) to higher spins, specifically spin-3. We find a special "chiral" point for the spin-three, analogous to the spin-two example, which actually coincides with the usual spin-two chiral point. But in contrast to usual TMG, there is the presence of a non-trivial trace and its logarithmic partner at the chiral point. The trace modes carry energy opposite in sign to the traceless modes. The logarithmic partner of the traceless mode carries negative energy indicating an instability at the chiral point. We make several comments on the asymptotic symmetry and its possible deformations at this chiral point and speculate on the higher spin generalisation of LCFT2 dual to the spin-3 massive gravity at the chiral point.