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arXiv · 1211.4454

Semi-classical unitarity in 3-dimensional higher-spin gravity for non-principal embeddings

H. Afshar·M. Gary·D. Grumiller·R. Rashkov·M. Riegler
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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.

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H. Afshar, M. Gary, D. Grumiller, R. Rashkov, M. Riegler. 2012-11-26. Semi-classical unitarity in 3-dimensional higher-spin gravity for non-principal embeddings. https://doi.org/10.1088/0264-9381%2F30%2F10%2F104004

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