Asymptotic symmetries and thermodynamics of higher spin black holes inAdS3

Abstract

We study black holes carrying higher spin charge in AdS 3 within the framework of SL(N, R) × SL(N, R) Chern-Simons theory. Focussing attention on the N = 4 case, we explicitly analyze the asymptotic symmetry algebra of black hole solutions with a chemical potential for spin-four charge. We demonstrate that the background describes an RG flow between an IR fixed point with W 4 symmetry and a UV fixed point with W-symmetry associated to a non-principal embedding of sl(2) in sl(4). Matching Chern-Simons equations with Ward identities of the deformed CFT, we show that the UV stress tensor is twisted by a certain U(1) current, and the flow is triggered by an operator with dimension 4/3 at the UV fixed point. We find independent confirmation of this picture via a consistent formulation of thermodynamics with respect to this UV fixed point. We further analyze the thermodynamics of multiple branches of black hole solutions for N = 4, 5 and find that the BTZ-branch, dominant at low temperatures, ceases to exist at higher temperatures following a merger with a thermodynamically unstable branch. We also point out an interesting connection between the RG flows and generalized KdV hierarchies.

Conformal perturbation theory and higher spin entanglement entropy on the torus

“…3 On the other hand, the holographic duals to such states which are the spin-three black holes of [13,14] appear to display an RG flow from an IR AdS3 geometry with W∞[λ] symmetry [38][39][40] to a UV AdS3 with different (non-principal) asymptotic W-algebra symmetry [41]. Several works have pointed out both the intriguing consequences of this picture [42,43], and possibly the complete absence of an RG flow interpretation [44,45].…”

$ \mathcal{W} $ symmetry and integrability of higher spin black holes

“…Black holes carrying higher spin charges have also been found [46]. Their spacetime structure has been discussed [39] and their thermodynamics has been investigated [46][47][48][49][50][51][52][53]. The phase structure of black holes was further explored in [54][55][56].…”

About the phase space of SL(3) black holes

“…This time the constraints will look like 12) JHEP03 (2015)081 and the corresponding first order in µ 3 corrections to (3.10) are…”

“…From the first line in (2.9) and after imposing the second class constraints (2.2) and (2.3) we arrive to 12) which after taking Λ = δ 2 τ a , A 1 = A b 1 τ b reduces to the Kac-Moody algebra…”

“…Higher spin theories [2][3][4][5][6] in 3D, have been of great interest recently, and specifically, the study of higher spin black holes in the Chern-Simons formulation has been one of the most active lines of research [1,[7][8][9][10][11][12][13][14][15][16][17][18].…”