Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Smoothed Transitions in Higher Spin AdS Gravity

Shamik Banerjee, Alejandra Castro, Simeon Hellerman, Eliot Hijano, Arnaud Lepage-Jutier, Alexander Maloney, Stephen Shenker

TL;DR

The paper investigates the thermodynamics of higher spin AdS/CFT duals by analyzing the λ→0 limit of W_N minimal models and CS-matter on T^2. It shows that the boundary partition function reduces to that of N−1 free bosons, due to a continuous orbifold description, and that a dense continuum of light states smooths out the Hawking-Page transition in the bulk, with a logarithmic entropy growth S ∼ (N/2) log(T/λ^2). The bulk interpretation involves a continuum of conical defects or topological sectors that dominate at low temperatures, challenging the conventional single-saddle picture of AdS thermodynamics. Overall, the work suggests a fundamentally quantum-mechanical/topological nature for the light sector in higher-spin gravity and motivates further study of bulk solution spaces and genus-variant holography.

Abstract

We consider CFTs conjectured to be dual to higher spin theories of gravity in AdS_3 and AdS_4. Two dimensional CFTs with W_N symmetry are considered in the lambda=0 (k --> infinity) limit, where they are conjectured to be described by continuous orbifolds. The torus partition function is computed, using reasonable assumptions, and equals that of a free field theory. We find no phase transition at temperatures of order one; the usual Hawking-Page phase transition is removed by the highly degenerate light states associated with conical defect states in the bulk. Three dimensional Chern-Simons-matter CFTs with vector-like matter are considered on T^3, where the dynamics is described by an effective theory for the eigenvalues of the holonomies. Likewise, we find no evidence for a Hawking-Page phase transition at large level k.

Smoothed Transitions in Higher Spin AdS Gravity

TL;DR

The paper investigates the thermodynamics of higher spin AdS/CFT duals by analyzing the λ→0 limit of W_N minimal models and CS-matter on T^2. It shows that the boundary partition function reduces to that of N−1 free bosons, due to a continuous orbifold description, and that a dense continuum of light states smooths out the Hawking-Page transition in the bulk, with a logarithmic entropy growth S ∼ (N/2) log(T/λ^2). The bulk interpretation involves a continuum of conical defects or topological sectors that dominate at low temperatures, challenging the conventional single-saddle picture of AdS thermodynamics. Overall, the work suggests a fundamentally quantum-mechanical/topological nature for the light sector in higher-spin gravity and motivates further study of bulk solution spaces and genus-variant holography.

Abstract

We consider CFTs conjectured to be dual to higher spin theories of gravity in AdS_3 and AdS_4. Two dimensional CFTs with W_N symmetry are considered in the lambda=0 (k --> infinity) limit, where they are conjectured to be described by continuous orbifolds. The torus partition function is computed, using reasonable assumptions, and equals that of a free field theory. We find no phase transition at temperatures of order one; the usual Hawking-Page phase transition is removed by the highly degenerate light states associated with conical defect states in the bulk. Three dimensional Chern-Simons-matter CFTs with vector-like matter are considered on T^3, where the dynamics is described by an effective theory for the eigenvalues of the holonomies. Likewise, we find no evidence for a Hawking-Page phase transition at large level k.

Paper Structure

This paper contains 8 sections, 65 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Free theory analysis in (1+1) dimensions
  3. Spectrum revisited
  4. Implications for AdS$_3$ Higher Spin Gravity
  5. Chern-Simons Matter analysis in (2+1)-dimensions
  6. Discussion
  7. Measure factor
  8. Gas of Free Higher Spin Particles

Figures (2)

  • Figure 1: The density of light states $\rho(\Delta)$ for large $k$, denoted by plusses. From left to right we have $(N=3,k=10^3)$, $(N=4,k=500)$ and $(N=5,k=100)$. The dashed line corresponds to the fit $\rho(\Delta)\sim \Delta^{(N-3)/2}$. The sharp deviation at large $\Delta$ indicates that, above a critical value of $\Delta$, non-light states give important contributions to the spectrum.
  • Figure 2: $Z$ as a function of $T$ for $N=3,4$. Scale on both axis are logarithmic. The straight line is the fit $\log Z= (N-1)/2\log T+{\rm constant}$.