Higher spin Chern–Simons theory and the super Boussinesq hierarchy

In this paper, we construct a map between a solution of supersymmetric Chern–Simons higher spin gravity based on the superalgebra [Formula: see text] with Lifshitz scaling and the [Formula: see text] 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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