Gauge-invariant Lagrangians for mixed-antisymmetric higher spin fields

TL;DR

This paper develops gauge-invariant Lagrangian formulations for mixed-antisymmetric higher-spin fields in flat space using a BRST approach, extending previous results and providing a foundation for interacting theories.

Contribution

It introduces a Lorentz-invariant BRST-based method to construct gauge-invariant Lagrangians for mixed-antisymmetric higher-spin fields with reducibility, generalizing prior work.

Findings

Constructed gauge-invariant Lagrangians for mixed-antisymmetric higher-spin fields.

Provided a minimal BRST--BV action suitable for interactions.

Extended previous formulations to include reducible gauge parameters.

Abstract

Lagrangian descriptions of irreducible and reducible integer higher-spin representations of the Poincare group subject to a Young tableaux $Y[\hat{s}_1,\hat{s}_2]$ with two columns are constructed within a metric-like formulation in a $d$-dimensional flat space-time on the basis of a BRST approach extending the results of [arXiv:1412.0200[hep-th]]. A Lorentz-invariant resolution of the BRST complex within both the constrained and unconstrained BRST formulations produces a gauge-invariant Lagrangian entirely in terms of the initial tensor field $\Phi_{[\mu]_{\hat{s}_1}, [\mu]_{\hat{s}_2}}$ subject to $Y[\hat{s}_1,\hat{s}_2]$ with an additional tower of gauge parameters realizing the $(\hat{s}_1-1)$-th stage of reducibility with a specific dependence on the value $(\hat{s}_1-\hat{s}_2)=0,1,...,\hat{s}_1$. Minimal BRST--BV action is suggested, being proper solution to the master equation in the minimal sector and providing objects appropriate to construct interacting Lagrangian formulations with mixed-antisymmetric fields in a general framework.