Towards Lagrangian formulations of mixed-symmetry Higher Spin Fields on AdS-space within BFV-BRST formalism

TL;DR

This paper develops a gauge-invariant Lagrangian framework for mixed-symmetry higher-spin fields in AdS spaces using BFV-BRST formalism, facilitating the description of complex higher-spin spectra in string theory.

Contribution

It introduces a novel approach combining Verma modules, oscillator realizations, and BFV-BRST operators for describing mixed-symmetry higher-spin fields in AdS.

Findings

Constructed gauge-invariant Lagrangians for higher-spin fields.

Applied BFV-BRST formalism to non-linear algebras in AdS.

Provided a systematic method for higher-spin field analysis.

Abstract

The spectrum of superstring theory on the $AdS_5 \times S_5$ Ramond-Ramond background in tensionless limit contains integer and half-integer higher-spin fields subject at most to two-rows Young tableaux $Y(s_1,s_2)$. We review the details of a gauge-invariant Lagrangian description of such massive and massless higher-spin fields in anti-de-Sitter spaces with arbitrary dimensions. The procedure is based on the construction of Verma modules, its oscillator realizations and of a BFV-BRST operator for non-linear algebras encoding unitary irreducible representations of AdS group.