Gauge Invariant Lagrangians for Free and Interacting Higher Spin Fields. A Review of the BRST formulation

TL;DR

The work develops a BRST-based program to construct gauge-invariant Lagrangians for free and interacting higher-spin fields in Minkowski and AdS spaces, using a nilpotent BRST charge $Q$ with $Q^2=0$. It builds both reducible and irreducible representations for massless and massive fields via oscillator/BRST formalisms and dimensional reduction, yielding Fronsdal-like Lagrangians and triplet formalisms. It then introduces a BRST-invariant cubic vertex with explicit flat-space and AdS realizations and even an exact all-orders vertex, illustrating explicit spin-1 and spin-2 examples and their gauge transformations. The framework connects to open-string field theory structures and ambient-space techniques, offering a versatile toolkit for higher-spin gauge theories, holography, and consistency in curved backgrounds.

Abstract

We give a detailed review of the construction of gauge invariant Lagrangians for free and interacting higher spin fields using the BRST approach developed over the past few years.