Abstract
We provide a simple holographic description for a warped conformal field theory (WCFT) at finite temperature. To this end we study the counterpart of warped anti-de Sitter black holes in three dimensions using a lower-spin $\mathfrak{sl}(2,\mathbb{R})\oplus\mathfrak{u}(1)$ Chern-Simons theory proposed by Hofman and Rollier. We determine the asymptotic symmetries, thermal entropy and holographic entanglement entropy and show that all these quantities are in perfect agreement with the expectations from the dual WCFT perspective. In addition we provide a metric interpretation of our results which naturally fits with our analysis in the Chern-Simons formulation.
Highlights
For the largest part of their existence, anti–de Sitter (AdS) spaces and conformal field theories (CFTs) have followed fairly independent and lonesome paths
This important step establishing a link between AdS and CFT led to unexpected breakthroughs in gravitational physics, such as the beautiful interplay between twodimensional CFTs and black hole entropy, which crystallizes in the famous Cardy formula [5,6,7,8] and eventually culminates in the AdS=CFT correspondence [9,10,11]
III, we show how to define the vacuum state of our configuration in the Chern-Simons formulation and give supporting arguments for the requirement (1.2) using warped conformal field theory (WCFT) arguments as well as (1.4)
Summary
For the largest part of their existence, anti–de Sitter (AdS) spaces and conformal field theories (CFTs) have followed fairly independent and lonesome paths. We will identify the gauge connection counterparts of WAdS3 black holes, study their thermodynamics and compare to the predictions from WCFT Another motivation to study warped black hole solutions in lower-spin gravity is related to its similarity to higherspin gravity theories in AdS3 that can be described in terms of a Chern-Simons connection with a specific gauge algebra (see e.g., [62,63,64,65]). In the Chern-Simons formulation, this is usually done by requiring that the holonomies of the gauge connection satisfy certain requirements (see e.g., [66,67]) These requirements are basically that the holonomies of the higher-spin connections have the same eigenvalues as the corresponding connection describing the BTZ black hole in AdS3. In Appendix A, we summarized how the usual BTZ black holes are described in the metric formulation as well as in the Chern-Simons formulation with slð; RÞ ⊕ slð; RÞ gauge symmetry
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