Gauge-invariant Lagrangians for mixed-antisymmetric higher spin fields

Abstract

Lagrangian descriptions of integer HS representations of the Poincare group subject to a Young tableaux $Y\left[ {{{\hat s}_1},{{\hat s}_2}} \right]$ with two columns are constructed within a metric-like formulation in a d-dimensional flat space-time on a basis of the BRST approach. A Lorentz-invariant resolution of the BRST complex within BRST formulations produces a gauge-invariant Lagrangian in terms of the initial tensor field ${\Phi _{{{\left[ \mu \right]}_{{{\hat s}_1},}}{{\left[ \mu \right]}_{{{\hat s}_2}}}}}$ subject to $Y\left[ {{{\hat s}_1},{{\hat s}_2}} \right]$ with an additional tower of gauge parameters realizing the $\left( {{{\hat s}_1} - 1} \right)$-th stage reducible theory with a specific dependence on the value $\left( {{{\hat s}_1} - {{\hat s}_2}} \right) = 0,1, \ldots {\hat s_1}$. Minimal BRST–BV action is suggested, providing objects appropriate to construct interacting models with mixed-antisymmetric fields in a general framework.