Higher-Spin Gauge Interactions for Matter Fields in Two Dimensions

TL;DR

The work addresses constructing a two-dimensional higher-spin gauge theory that couples to boson and fermion matter in an integrable framework. It introduces an explicit HS gauge formulation based on an associative algebra and its extension, yielding zero-curvature equations from a BF-type action in an $AdS_2$ background and an unfolded covariant-constancy description of matter. The linearized analysis reproduces Klein-Gordon-type dynamics for matter with mass parameter $m^2=\mu$, while the full nonlinear theory remains integrable due to the infinite HS multiplet; matter contributions enter quadratically in the gravitational sector without imposing current constraints. This 2D construction offers a tractable arena to study exact HS interactions, clarifies links to $W_{1+\infty}$ structures, and sets the stage for diagonalization and generalization to arbitrary masses in $AdS_2$.

Abstract

We formulate a new model which describes higher-spin gauge interactions for matter fields in two dimensions. This model is a higher-spin generalization of d2 gravity and turns out to be integrable. No vanishing higher-spin current conditions are imposed on the matter fields.