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

A bstract 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 $$ \mathfrak{\max}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>max</mml:mo> </mml:math> - $$ \mathfrak{bm}{\mathfrak{s}}_3 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>bm</mml:mi> <mml:msub> <mml:mi>s</mml:mi> <mml:mn>3</mml:mn> </mml:msub> </mml:math> algebra, which in turn corresponds the asymptotic symmetries of the Maxwell CS gravity. We also show that the $$ \mathfrak{h}{\mathfrak{s}}_3\mathfrak{\max} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>h</mml:mi> <mml:msub> <mml:mi>s</mml:mi> <mml:mn>3</mml:mn> </mml:msub> <mml:mo>max</mml:mo> </mml:math> - $$ \mathfrak{bm}{\mathfrak{s}}_3 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>bm</mml:mi> <mml:msub> <mml:mi>s</mml:mi> <mml:mn>3</mml:mn> </mml:msub> </mml:math> algebra can alternatively be obtained as a vanishing cosmological constant limit of three copies of the $$ {\mathcal{W}}_3 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>W</mml:mi> <mml:mn>3</mml:mn> </mml:msub> </mml:math> algebra, with three independent central charges.