Boundary dynamics of asymptotically flat 3D gravity coupled to higher spin fields

Abstract

We construct a two-dimensional action principle invariant under a spin-three extension of BMS${}_3$ group. Such a theory is obtained through a reduction of Chern-Simons action with a boundary. This procedure is carried out by imposing a set of boundary conditions obtained from asymptotically flat spacetimes in three dimensions. When implementing part of this set, we obtain an analog of chiral WZW model based on a contraction of $sl(3,\mathbb{R})\times sl(3,\mathbb{R})$. The remaining part of the boundary conditions imposes constraints on the conserved currents of the model, which allows to further reduce the action principle. It is shown that a sector of this latter theory is related to a flat limit of Toda theory.

16 pages, no figures

References in corpus (5)

• Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
• Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity
• The BMS/GCA correspondence
• Entropy of three-dimensional asymptotically flat cosmological solutions
• Flat-Space Chiral Gravity

Cited by in corpus (3)

• Geometric actions for three-dimensional gravity
• Higher spin extension of cosmological spacetimes in 3D: asymptotically flat behaviour with chemical potentials and thermodynamics
• Vacuum energy in asymptotically flat 2+1 gravity