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

TL;DR

The paper develops a nonlinear higher-spin gauge theory in $d=3$ AdS space that couples HS gauge fields to massive spin-0 and spin-1/2 matter, with the matter content organized into $N=2$ hypermultiplets and masses arising from auxiliary-field vevs. It employs unfolded covariant-constancy equations, a deformed oscillator realization, and a Moyal star-product to build a self-consistent HS system that admits both unitary unitary inner YM truncations and discrete symmetry reductions to $N=1$ SUSY; massless and massive sectors are connected via a nonlocal integrating flow akin to Nicolai/Bäcklund mappings. The work demonstrates that the full HS dynamics can be extended to non-Abelian inner symmetries, constructs a rich landscape of truncations (orthogonal, symplectic, unitary), and reveals a nonlocal flow that relates nonlinear HS solutions to linearized ones, with implications for higher-dimensional HS theories and potential links to M-theory. Overall, the model provides explicit mechanisms for mass generation, global supersymmetry structure, and a formal integrating flow that may illuminate locality questions in HS gauge theories and their holographic interpretations. The results suggest a deep interplay between nonlocality, cosmological constant, and HS interactions in a setting that parallels string/M-theory perspectives on HS towers and their low-energy limits.

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 Bäcklund-Nicolai-type mapping to the free system.