The semiclassical limit of W N CFTs and Vasiliev theory

Abstract

We propose a refinement of the Gaberdiel-Gopakumar duality conjecture between W N conformal field theories and 2+1-dimensional higher spin gravity. We make an identification of generic representations of the W N CFT in the semiclassical limit with bulk configurations. By studying the spectrum of the semiclassical limit of the W N theories and mapping to solutions of Euclidean Vasiliev gravity at λ = −N , we propose that the 'light states' of the W N minimal models in the 't Hooft limit map not to the conical defects of the Vasiliev theory, but rather to bound states of perturbative scalar fields with these defects. Evidence for this identification comes from comparing charges and from holographic relations between CFT null states and bulk symmetries. We also make progress in understanding the coupling of scalar matter to sl(N ) gauge fields.

Phase structure of higher spin black holes

“…Though a unitary CFT dual to these system with finite spin is not known (interesting non-unitary CFT dual to finite spin systems have been worked out in [20,21]) yet but if we extrapolate the results from the above mentioned works, then the transition temperature should be O( √ N ) ∼ O (1) which is what we obtain. Secondly these systems by similar argument cannot have a huge spectrum of light states which smoothen out these transitions and hence there is no barrier for these transitions to take place.…”

“…Based on this, a duality between higher spin theories in AdS 3 and CFT with W-symmetry was proposed in [17]. Further elaborations of the proposal were done [18][19][20][21] and for a review see [22]. The topologically massive versions of these higher spin theories and their possible dualities to logarithmic CFTs was shown in [23][24][25][26].…”

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].…”

Multi-centered AdS3 solutions from Virasoro conformal blocks

“…As we shall see, this is actually not possible without introducing extra spurious singularities in the differential equation, which as discussed in section 3.3 correspond to extra pointlike sources with negative masses. As reviewed there, these sources do have a dual CFT interpretation as describing insertions of degenerate primaries [36][37][38]. The corresponding solutions can be simply written down analytically.…”