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

A bstract Massless higher-spin fields show no preference for any value of the cosmological constant in 3 d . 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+ ∞ . 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 that is perturbatively local. 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.