A new higher-spin theory of supergravity in 2+1 dimensions

Abstract: We construct a novel higher-spin theory of gravity in 2+1 spacetime dimensions. The construction is based on a higher-spin super-algebra extending the Poincare group. Our algebra accommodates all integer and half-integer spins from 1 to infinity and, in contrast to the results in the existing literature, allows for an infinite number of particles of spin s. Subsequently, we generalise the construction to include a cosmological constant. In this case, the higher-spin group is an extension of the AdS or dS group and contains only bosonic generators. Treating the higher-spin groups as gauge groups we write down the Chern-Simons like action, the transformation laws for the fields of the theory and their equations of motion in each of the three aforementioned cases. Finally, we comment on the generalisation of our algebras in $d+1$ dimensions.