Gauge-invariant Lagrangians for mixed-antisymmetric higher spin fields

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.

8 pages, extended Contribution to the Proceedings of the International Workshop "Supersymmetry and Quantum Symmetries" (SQS'2015, August 3 - August 8, 2015, Dubna, Russia); corrections in (4),(19) were made; ref.25, footnote 1 added; acknowledgements, footnote 2 with comments on gauge transformations in [28, 29] updated; resulting actions (18), (19) corrected

References in corpus (5)

• Gauge Invariant Lagrangians for Free and Interacting Higher Spin Fields. A Review of the BRST formulation
• Frame-like Actions for Massless Mixed-Symmetry Fields in Minkowski space
• Gauge invariant Lagrangian construction for massive bosonic mixed symmetry higher spin fields
• Higher-Spin Theory and Space-Time Metamorphoses
• BRST-BFV Lagrangian Formulations for Higher Spin Fields subject to two-column Young Tableaux

Cited by in corpus (5)

• Weyl Action of Two-Column Mixed-Symmetry Field and Its Factorization Around (A)dS Space
• BRST-BFV and BRST-BV Descriptions for Bosonic Fields with Continuous Spin on $R^{1,d-1}$
• BRST-BV Quantum Actions for Constrained Totally-Symmetric Integer HS Fields
• Consistent Lagrangians for irreducible interacting higher-spin fields with holonomic constraints
• Massive two-column bosonic fields in the frame-like formalism