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

TL;DR

This paper demonstrates the possibility of constructing unitary semi-classical higher-spin gravity theories in three dimensions with non-principal embeddings, challenging previous beliefs about their unitarity limitations.

Contribution

It introduces a method to achieve unitarity in non-principal embedding higher-spin theories using Feigin-Semikhatov algebras, allowing large central charges.

Findings

Constructed infinite families of unitary theories at rational Chern-Simons levels.

Achieved arbitrarily large central charges up to c = N/4 - 1/8 - O(1/N).

Confirmed recent theoretical speculation about unitarity in these models.

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.