Higher Spin Chern-Simons Theory and the Super Boussinesq hierarchy (1709.02345v1)

Published 7 Sep 2017 in hep-th, math-ph, and math.MP

Abstract: In this paper we construct a map between a solution of supersymmetric Chern-Simons higher spin gravity based on the superalgebra $sl(3|2)$ with Lifshitz scaling and the $N=2$ super Boussinesq hierarchy. We show that under this map the time evolution equations of both theories coincide. In addition, we identify the Poisson structure of the Chern-Simons theory induced by gauge transformation with the second Hamiltonian structure of the super Boussinesq hierarchy.

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