Smoothed transitions in higher spin AdS gravity

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 λ = 0 (k → ∞) 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.

Phase structure of higher spin black holes

“…So, there are no thermodynamically stable large black holes at temperatures of O(1) in this system. Similar study was undertaken in W ∞ [0] CFTs in 2 dimensions in [48] and they found similar results. This was attributed to the presence of a very huge spectrum of light states in these CFTs which smoothen out the phase transition.…”

Phases of large N vector Chern-Simons theories on S 2 × S 1

“…It would of course be more satisfactory to rederive all our conclusions from computations that utilize temporal gauge all the way through. This would also allow the evaluation of the partition function of Chern-Simons theory on arbitrary genus g surfaces at finite values of the temperature [21,25]. The main obstruction to this procedure are a set of spurious divergences that appear in computations in matter Chern-Simons theories in temporal gauge [16]; it may prove possible to understand these divergences well enough to deal with them.…”

“…It is a famous result in the study of non abelian solitons that the winding number of the map H(φ) is the same as the wrapping number of the map from S 2 toS 3 defined by U (x). 25 Clearly the function H(φ) can be chosen to be a constant (so that the gauge transformation g(θ, φ) is well defined on the south pole) only if its winding number vanishes. It follows that the gauge choice (ii) can be implemented by a smooth gauge function g(x) if and only if the wrapping number of U (x) on S 2 vanishes.…”

“…[16,18,19,20,21,17,22,23,24,25,26,27]). In particular it has been argued in the important recent paper [27] that the entire effect of matter loops on gauge dynamics, at temperatures of order √ N and at leading order in N , is to generate a term of the form…”

Comments on Rényi entropy in AdS3/CFT2

“…While they possess the right algebras, they either fail to be unitary [43,61] or spectrally sparse [10,62,63] depending on the precise large c limit taken. In the better-studied 't Hooft limit, these theories have a near-continuum of light states below the gap that grows exponentially with c. These states pollute the large c factorization properties of the theory and wash out any bulk phase transitions [63,64]. It is fair to say that the precise holographic dictionary with the Vasiliev theory has yet to be fully understood.…”