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Dualities from higher-spin supergravity

We study the vacuum structure of spin-3 higher-spin supergravity in AdS_3 spacetime. The theory can be written as a Chern-Simons theory based on the Lie superalgebra sl(3|2). We find three distinct AdS_3 vacua, AdS^(1), AdS^(2) and AdS^(p), each corresponding to one embedding of the osp(1|2) subalgebra into the sl(3|2) algebra. We explicitly construct the RG flows from AdS^(1) to AdS^(p) and from AdS^(2) to AdS^(p), which identifies AdS^(p) as an IR vacuum and AdS^(1), AdS^(2) as two different UV vacua. Thus a duality is found between the two UV theories in the sense that the two theories, each with a chemical potential turned on, flow to the same IR theory. Moreover, we identify a similar structure in the Hamiltonian reductions of the 2d Wess-Zumino-Witten (WZW) model with sl(3|2)-valued currents by matching the chiral symmetries there with the asymptotic symmetries of the three different embeddings. Our computation gives an RG interpretation of (certain types of) the Hamiltonian reductions. In addition, it gives a hint of a duality between the 3d higher-spin supergravity and some conformally extended super-Toda theory as suggested by Mansfield and Spence for the bosonic case.