Matter-coupled higher spin gravities in 3d: no- and yes-go results

TL;DR

This paper investigates matter coupling in 3D higher-spin gravities, showing no nontrivial interactions in most cases but constructing an exotic matter-coupled theory with auxiliary fields that admits a flat limit and potential holographic duality.

Contribution

It extends matter coupling results to flat space and constructs an exotic matter-coupled higher-spin theory in (A)dS3 with a Poisson sigma-model structure.

Findings

No nontrivial higher-order deformations in flat and (A)dS3 spaces.

Constructed an exotic matter-coupled theory with auxiliary fields.

The theory admits a flat limit and has a Poisson sigma-model form.

Abstract

Massless higher-spin fields show no preference for any value of the cosmological constant in $3d$. All matter-free higher-spin gravities in 3d are equivalent to Chern-Simons theories with an appropriate choice of gauge algebra. For various reasons, including holography, it is important to enrich them with matter fields. In $(A)dS_3$, the coupling of matter fields to higher-spin fields is well-known to the leading order and is determined by the representation theory. We extend this result to flat space, where the relevant higher-spin algebra is the Poisson algebra, aka $w_{1+\infty}$. However, we show that both in flat and $(A)dS_3$ spaces there are no nontrivial higher order deformations/interactions. Nevertheless, by enlarging the field content with some auxiliary fields and taking advantage of the chiral higher-spin gravity's vertices, it is possible to construct an exotic matter-coupled theory on $(A)dS_3$. It also admits a flat limit. The equations of motion have the form of a Poisson sigma-model and a meaningful action has the form of a Courant sigma-model. We also explore the potential for embedding this theory into a holographic duality.