Higher spin theory in 3-dimensional flat space

TL;DR

We present the first explicit construction of a non-trivial higher spin theory in three-dimensional flat space, focusing on spin-3 gravity formulated as a Chern-Simons theory with flat-space boundary conditions. The resulting boundary charges form a finite, integrable algebra whose canonical realization yields a novel centrally extended flat-space spin-3 BMS-like symmetry, with $c_L=0$ and $c_M=12k$, obtained as an İnönü–Wigner contraction of two copies of $W_3$. The work further discusses flat-space cosmologies and the potential for higher-spin deformations and generalizations to arbitrary hs theories, linking to holography in flat space. It thus provides a concrete setting to study higher-spin holography beyond AdS and paves the way for exploring unitary issues, cosmological solutions, and connections to string theory in the flat-space limit.

Abstract

We present the first example of a non-trivial higher spin theory in 3-dimensional flat space. We propose flat-space boundary conditions and prove their consistency for this theory. We find that the asymptotic symmetry algebra is a (centrally extended) higher spin generalization of the Bondi- Metzner-Sachs algebra, which we describe in detail. We also address higher spin analogues of flat space cosmology solutions and possible generalizations.