Higher-spin gauge interactions for massive matter fields in 3D AdS space-time Original Research Article

A remarkable feature of the models with interactions exhibiting higher-spin (HS) gauge symmetries in d > 2 is that their most symmetric vacua require the (anti)-de Sitter (AdS) geometry rather than the flat geometry. 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-12 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 3d N = 2 massive hypermultiplets in certain representations of U(n) × 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.