Semi-classical unitarity in 3-dimensional higher-spin gravity for non-principal embeddings
arXiv:1211.4454 · doi:10.1088/0264-9381/30/10/104004
Abstract
Higher-spin gravity in three dimensions is efficiently formulated as a Chern-Simons gauge-theory, typically with gauge algebra sl(N)+sl(N). The classical and quantum properties of the higher-spin theory depend crucially on the embedding into the full gauge algebra of the sl(2)+sl(2) factor associated with gravity. It has been argued previously that non-principal embeddings do not allow for a semi-classical limit (large values of the central charge) consistent with unitarity. In this work we show that it is possible to circumvent these conclusions. Based upon the Feigin-Semikhatov generalization of the Polyakov-Bershadsky algebra, we construct infinite families of unitary higher-spin gravity theories at certain rational values of the Chern-Simons level that allow arbitrarily large values of the central charge up to c = N/4 - 1/8 - O(1/N), thereby confirming a recent speculation by us 1209.2860.
20 pp in CQG style, 1 eps figure, v2: added labels in Fig. and 1 Ref
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- Lobachevsky holography in conformal Chern-Simons gravity
- Asymptotic Symmetries of Colored Gravity in Three Dimensions
- Flat space holography in spin-2 extended dilaton-gravity
- Unitary W-algebras and three-dimensional higher spin gravities with spin one symmetry
- Null warped AdS in higher spin gravity