Asymptotic structure of three-dimensional Maxwell Chern-Simons gravity coupled to spin-3 fields

Abstract

In this work we analyze the asymptotic symmetries of the three-dimensional Chern-Simons (CS) gravity theory for a higher spin extension of the so-called Maxwell algebra. We propose a generalized set of asymptotic boundary conditions for the aforementioned flat gravity theory and we show that the corresponding charge algebra defines a higher-spin extension of the $\mathfrak{max}$-$\mathfrak{bm}{\mathfrak{s}}_3$ algebra, which in turn corresponds the asymptotic symmetries of the Maxwell CS gravity. We also show that the $\mathfrak{h}{\mathfrak{s}}_3\mathfrak{max}$-$\mathfrak{bm}{\mathfrak{s}}_3$ algebra can alternatively be obtained as a vanishing cosmological constant limit of three copies of the ${\mathcal{W}}_3$ algebra, with three independent central charges.