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 [ŝ 1 ,ŝ 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 fieldwith an additional tower of gauge parameters realizing the (ŝ 1 − 1)-th stage of reducibility with a specific dependence on the value (ŝ 1 −ŝ 2 ) = 0, 1, ...,ŝ 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.

Constrained BRST-BFV Lagrangian formulations for higher spin fields in Minkowski spaces

“…Another direct consequence from the procedure of constrained Lagrangian formulation for halfinteger HS fields concerns, the equivalence among the unconstrained BRST Lagrangian formulation developed in [38], [37] and constrained BRST Lagrangian formulations for the integer HS irreducible representations of the Poincare group in Minkowski space-time with fixed generalized spin (s) k = (s 1 , s 2 , ..., s k ), s i ≥ s j , i > j. and constrained BRST Lagrangian formulation, in fact, suggested here in full details (considered without spin operator for totally-symmetric case in [44] and for mixed-symmetric case in [45]).…”

“…There exists so-called Maxwell-like formulations for metric-like tensor fields (on flat and to some extent on (A)dS spaces) developed originally with off-shell differential constraints on the gauge parameters and with their resolution by means of a tower of reducible gauge transformations with higher derivatives [34]. We recall that irreducible Poincare or (A)dS group representations in constant curvature space-times is described by mixedsymmetric (MS) HS fields with an arbitrary Young tableaux of k rows, Y (s 1 , ..., s k ) (symmetric basis), determined by more than one spin-like parameters s i [35], [36], and, equivalently, by mixed-antisymmetric (spin-)tensor fields with an arbitrary Young tableaux of l columns, Y [ŝ 1 , ...,ŝ l ] (antisymmetric basis), the integers or half-integersŝ 1 ≥ŝ 2 ≥ ... ≥ŝ l having a spin-like interpretation [37]. BRST-BFV Lagrangian formulations for arbitrary free MS HS fields with integer and half-integer spins were constructed in an unconstrained form (complete with all the algebraic constraints that follow from the Lagrangian and the tower of the respective gauge transformations after a partial gauge fixing) in our papers [38], [39].…”

Massive two-column bosonic fields in the frame-like formalism

“…BRST approach for the general massive mixed symmetry fields have been developed in[13,14] (see also[15,16] for the two-column case), while frame-like gauge invariant description for the massive two-raw fields were given in[17,18]. Weyl actions and their possible AdS and massive deformations for the two-column fields have been considered recently in[19].…”