Progress in Higher Spin Gauge Theories

TL;DR

The paper surveys progress in four-dimensional higher spin gauge theories, arguing that a consistent, fully interacting HS theory requires an AdS$_4$ background and an infinite tower of spins organized by a Weyl (star-product) algebra. It presents a Vasiliev-type framework with HS connections $\omega(Y|x)$ and Weyl 0-forms $C(Y|x)$, provides a concrete AdS$_4$ HS action, and develops an unfolded formulation that encodes all spins via nonlinear equations on an extended auxiliary space. It also extends the unfolded approach to 4d conformal HS theory, showing how conformal HS constraints can be organized and potentially deformed to yield a nonlinear theory related to AdS HS via compensators. Together, these results establish a covariant, nonlocal-in- spacetime but local-in-spinor-space structure for HS dynamics and point toward non-Abelian HS generalizations and string-theoretic connections in AdS/CFT contexts.

Abstract

General properties of the theory of higher spin gauge fields in $AdS_4$ are discussed. Some new results on the 4d conformal higher spin gauge theory are announced. Talk given at the International Conference "Quantization, Gauge Theory and Strings" in memory of E.S.Fradkin, Moscow, June 5-10, 2000.