Higher-Spin Gauge Theories in Four, Three and Two Dimensions

TL;DR

This work surveys the landscape of higher-spin gauge theories across $3+1$, $2+1$, and $1+1$ dimensions, highlighting the unfolded formulation as a unifying framework that encodes dynamics through zero-curvature conditions plus constraints. It presents explicit actions and equations for higher-spin fields in $3+1$ and $2+1$ dimensions, and introduces integrable models in $1+1$ dimensions with matter, including a BF-type action in AdS$_2$. A central theme is the role of infinite-dimensional higher-spin algebras, their star-product realizations, and the way AdS backgrounds enable nontrivial interactions while preserving gauge invariance. The paper also extends the algebraic framework to extended higher-spin superalgebras, classifies truncations leading to Yang–Mills substructures, and discusses connections to string theory and nonlocality, outlining key open problems for a fully nonperturbative action and quantum consistency.

Abstract

We review the theory of higher-spin gauge fields in four and three space-time dimensions and present some new results on higher-spin gauge interactions of matter fields in two dimensions.