3D Higher-Spin Gauge Theories with Matter

TL;DR

This work develops a 3D higher-spin gauge theory with matter in AdS3 using an unfolded framework based on the HS algebra hs(2;ν). The authors construct a nonlinear, nonlocal system of equations for generating functions W, B, and S and reveal an integrating flow in the coupling η that maps the full theory to free data, yielding a constructive perturbative solution. They demonstrate N=2 supersymmetry with a massive hypermultiplet, analyze truncations to N=1, and show how non-Abelian internal symmetries can be incorporated via matrix extensions, with mass formulas M^2_± = λ^2 ν(ν∓2)/2 for bosons and M^2_± = λ^2 ν^2/2 for fermions in the massive case. In the massless limit ν=0, higher N supersymmetries become realizable and internal symmetries can still be included, suggesting an integrability-like structure for these HS equations and potential links to broader M-theory contexts.

Abstract

This paper is a letter-type version of hep-th/9806236. We discuss properties of non-linear equations of motion which describe higher-spin gauge interactions for massive spin-0 and spin-1/2 matter fields in 2+1 dimensional anti-de Sitter space. The model is shown to have N=2 supersymmetry and to describe higher-spin interactions of d3 N=2 massive hypermultiplets. An integrating flow is found which reduces the full non-linear system to the free field equations via a non-local Bäcklund-Nicolai-type mapping.