Higher spin theories in AdS3 and a gravitational exclusion principle

Abstract

We consider theories of three dimensional quantum gravity in Anti-de Sitter space which possess massless higher-spin gauge symmetry. The perturbative spectrum of the theory includes higher spin excitations which can be organized into vacuum representations of the W N algebra; these are higher spin versions of the boundary gravitons. We describe a fundamental bound which relates the value of the cosmological constant to the amount of gauge symmetry present. In the dual CFT language, this is the statement that modular invariance implies that the theory can not be quantized unless the central charge is sufficiently large, i.e. if c ≥ N − 1. This bound relies on the assumption that all of the perturbative excitations exist as full states in the quantum theory, and can be circumvented if the theory possesses a linearization instability. The W N minimal models -recently conjectured to be dual to certain higher spin AdS theories by Gaberdiel and Gopakumar -provide an example of this phenomenon. This result can be regarded as an example of a "gravitational exclusion principle" in Anti-de Sitter space, where a non-perturbative quantum gravity mechanism involving black holes places a limit on the number of light degrees of freedom present. 1

Partition functions for higher-spin theories in AdS

“…6 Note: After an initial version of this paper appeared on the arXiv, we learned of [43,44,45], in which additional enhanced symmetries for higher-spin theories had been observed. 7 It is also possible that our results are related to these symmetries.…”

“…6 We thank M. Vasiliev for this observation. 7 We thank D. Sorokin for bringing this to our attention.…”

Effective action in a higher-spin background

“…It is intriguing that all known tests of the Klebanov-Polyakov conjecture circumvented successfully the lack of a variational principle [32][33][34][35][36][37]. Notice that the case of AdS 3 /CFT 2 is special in this respect [38][39][40][41][42]. In brief, a detailed analysis of the regularized effective action for free conformal scalars in a higher-spin background is motivated both by the induced gravity program and by the AdS/CFT correspondence.…”

Comments on Rényi entropy in AdS3/CFT2

“…A very similar calculation was done in [41] using traditional saddle point methods, and we utilize their approach here. The leading order result for the asymptotic growth of d N,n (h) in (3.19) is found to be…”