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.

arXiv comment16 pages, no figures

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• BMS Particles in Three Dimensions
• Geometric actions for three-dimensional gravity
• Higher spin extension of cosmological spacetimes in 3D: asymptotically flat behaviour with chemical potentials and thermodynamics
• Generalized Chern-Simons higher-spin gravity theories in three dimensions
• Dynamical structure of Carrollian Electrodynamics
• Integrable systems with BMS${}_3$ Poisson structure and the dynamics of locally flat spacetimes
• Three-dimensional Poincaré supergravity and $\mathcal{N}$-extended supersymmetric BMS${}_3$ algebra
• Semi-simple enlargement of the ${\mathfrak{bms}}_3$ algebra from a $\mathfrak{so}(2,2)\oplus \mathfrak{so}(2,1)$ Chern-Simons theory
• On the supersymmetric extension of asymptotic symmetries in three spacetime dimensions
• Asymptotic Symmetries of Maxwell Chern-Simons Gravity with Torsion
• Scalar Fields in 3D Asymptotically Flat Higher-Spin Gravity
• Equivalent Dual Theories for 3D N=2 Supergravity
• Vacuum energy in asymptotically flat 2+1 gravity
• Hietarinta Chern-Simons supergravity and its asymptotic structure
• Free-field construction of Carrollian $W_N$-algebras
• Asymptotic dynamics of three-dimensional gravity