On Higher Spin Theory: Strings, BRST, Dimensional Reductions

TL;DR

Problem: providing a consistent Lagrangian description of higher-spin fields in flat and curved backgrounds and clarifying their relation to string theory. Approach: a BRST quantization framework yields a triplet formulation for massless HS fields, and dimensional reduction generates massive HS theories in arbitrary dimensions; the method handles second-class constraints via auxiliary constructions and similarity transformations. Contributions: explicit derivations of massless HS Lagrangians from the BRST setup, full treatment of the dimensional reduction routes including flat-space and radial schemes, and discussion of extensions to AdS/dS backgrounds and supersymmetry. Significance: unifies higher-spin field theory with string theory perspectives, provides a practical route to construct and analyze massive HS theories in diverse backgrounds, and offers pathways toward supersymmetric HS models within string/M-theory contexts.

Abstract

We briefly review some modern developments in higher spin field theory and their links with superstring theory. The analysis is based on various BRST constructions allowing to derive the Lagrangians for massive and massless higher spin fields on flat or constant curvature backgrounds of arbitrary dimensions.