Aspects of Three-dimensional Spin-4 Gravity

TL;DR

This paper explores three-dimensional higher-spin gravity with a negative cosmological constant, constructing explicit solutions and analyzing their symmetries and thermodynamics to support the higher-spin holography framework.

Contribution

It provides the first explicit spin-4 generalization of the BTZ black hole solution and demonstrates the emergence of W_4 symmetry and consistent thermodynamics from bulk equations.

Findings

Constructed a spin-4 black hole solution in SL(4,R) Chern-Simons theory.

Showed the emergence of W_4 symmetry and higher-spin Ward identities.

Established a consistent thermodynamic interpretation matching Wilson loop eigenvalues.

Abstract

We discuss some interesting holographical aspects of three-dimensional higher-spin gravity with a negative cosmological constant in the framework of SL(4, R) \times SL(4, R) Chern-Simons theory. Using a recently found technique, we construct explicitly a solution that can be interpreted as spin-4 generalization of the BTZ solution, and demonstrate how W_4 symmetry and the higher-spin Ward identities arise from the bulk equations of motion coupled to spin-3 and spin-4 currents. We match the eigenvalues of a Wilson loop along the time-like direction of the BTZ to that of the spin-4 solution, and show that this yields remarkably consistent gravitational thermodynamics for the latter. This furnishes an important, concrete supporting example for a recent proposal to understand spacetime geometries in three-dimensional higher-spin gravity formulated via SL(N, R) \times SL(N, R) Chern-Simons theories.