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

TL;DR

This paper develops a new higher-spin supergravity theory in 2+1 dimensions using an extended super-algebra that includes all spins from 1 to infinity, generalizing to include cosmological constants and higher dimensions.

Contribution

It introduces a novel higher-spin super-algebra extending the Poincare group, accommodating infinite spins, and constructs a corresponding gauge theory with a Chern-Simons action.

Findings

Constructed a higher-spin super-algebra with all spins from 1 to infinity.

Formulated a Chern-Simons gauge theory based on the new algebra.

Extended the framework to include cosmological constants and higher 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.