Higher-Spin Theory - Part II: enter dimension three

TL;DR

This paper provides a pedagogical introduction to three-dimensional higher-spin theories, explaining their formulation via Chern-Simons actions and exploring current research directions in the field.

Contribution

It offers a clear, accessible overview of three-dimensional higher-spin theories, including their gauge formulation and recent research developments.

Findings

Formulation of 3D higher-spin theories using Chern-Simons actions

Review of current research and open problems in higher-spin gravity

Connection between higher-spin algebras and non-linear theories

Abstract

These notes aim at providing a pedagogical and pedestrian introduction to the subject and assume no previous knowledge apart from that of general relativity. We shall first recall the "frame" formulation of the later theory, then particularize it to three dimensions, and will end those preliminaries by reviewing the formulation of three-dimensional gravity as a gauge theory governed by a Chern-Simons action. An analogous path is then followed for higher-spin fields at the free level. Once the equivalent Chern-Simons action is established thereof, it is then explained how one can formulate three-dimensional higher-spin theories at the non-linear level by considering higher-spin Lie algebras. We then move on to commenting on what has already been done in the context of these theories and what interesting areas of research are currently under investigation.