Spin-3 Topological Massive Gravity
Bin Chen, Jiang Long, Jun-bao Wu

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 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 algebra and central charge .
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