Metric- and frame-like higher-spin gauge theories in three dimensions

Understand

We study the relation between the frame-like and metric-like formulation of higher-spin gauge theories in three space-time dimensions.

• We concentrate on the theory that is described by an SL(3) x SL(3) Chern-Simons theory in the frame-like formulation.
• The metric-like theory is obtained by eliminating the generalised spin connection by its equation of motion, and by expressing everything in terms of the metric and a spin-3 Fronsdal field.
• We give an exact map between fields and gauge parameters in both formulations.