Higher-Spin Gauge Interactions for Massive Matter Fields in 3D AdS Space-Time

TL;DR

This paper investigates higher-spin gauge interactions involving massive matter fields in 3D AdS space, revealing supersymmetric structures, gauge symmetries, and a non-local mapping to free systems, thus advancing understanding of HS models.

Contribution

It introduces a simple higher-spin model with massive matter in 3D AdS, demonstrating supersymmetry, gauge symmetries, and a non-local Bäcklund-Nicolai-type mapping, providing insights into HS theories.

Findings

Matter fields form N=2 hypermultiplets in specific gauge representations.

The model admits an integrating flow to a free system via a non-local mapping.

Supersymmetric truncations with O(n) and Sp(n) symmetries are constructed.

Abstract

A remarkable feature of the models with interactions exhibiting higher-spin (HS) gauge symmetries in $d>2$ is that their most symmetric vacua require (anti)-de Sitter (AdS) geometry rather than the flat one. In striking parallelism to what might be expected of M theory HS gauge theories describe infinite towers of fields of all spins and possess naturally space-time SUSY and Chan-Paton type inner symmetries. In this paper, we analyze at the level of the equations of motion the simplest non-trivial HS model which describes HS gauge interactions (on the top of the usual supergravitational and (Chern-Simons) Yang-Mills interactions) of massive spin-0 and spin-1/2 matter fields in d=2+1 AdS space-time. The parameter of mass of the matter fields is identified with the vev of a certain auxiliary field in the model. The matter fields are shown to be arranged into d3 N=2 massive hypermultiplets in certain representations of $U(n)\times U(m)$ Yang-Mills gauge groups. Discrete symmetries of the full system are studied, and the related N=1 supersymmetric truncations with O(n) and Sp(n) Yang-Mills symmetries are constructed. The simplicity of the model allows us to elucidate some general properties of the HS models. In particular, a new result, which can have interesting implications to the higher-dimensional models, is that our model is shown to admit an "integrating" flow that proves existence of a non-local B\"acklund-Nicolai-type mapping to the free system.