BRST Approach to Lagrangian Formulation of Bosonic Totally Antisymmetric Tensor Fields in Curved Space

Abstract

We apply the BRST approach, previously developed for higher spin field theories, to gauge invariant Lagrangian construction for antisymmetric massive and massless bosonic fields in arbitrary d-dimensional curved space. The obtained theories are reducible gauge models both in massless and massive cases and the order of reducibility grows with the value of the rank of the antisymmetric field. In both the cases the Lagrangians contain the sets of auxiliary fields and possess more rich gauge symmetry in comparison with standard Lagrangian formulation for the antisymmetric fields. This serves additional demonstration of universality of the BRST approach for Lagrangian constructions in various field models. 1 Aspects of modern state of higher spin field theory are discussed in the reviews [2]. 2 Recently this approach was applied to Lagrangian formulation of interacting bosonic higher spin gauge fields [9].

General Lagrangian formulation for higher spin fields with arbitrary index symmetry. I. Bosonic fields

“…One should be noted the case of totally antisymmetric tensors developed in Ref. [40] is contained in the general Lagrangian formulation for s 1 = s 2 = ... = s k = 1, k = [d /2].…”

“…4 there exists another realization of auxiliary Fock space generated by the fermionic oscillators (antisymmetric basis)â m µ m (x),ân + ν n (x) with anticommutation relations, {â m µ m ,â n+ ν n } = −η µ m ν n δ mn , for m, n = 1, ..., s 1 , and develop the procedure below following to the lines of Ref. [40] for totally antisymmetric tensors for s 1 = s 2 = ... = s k = 1.…”

Quartic interaction vertex in the massive integer higher spin field theory in a constant electromagnetic field

“…To derive the unconstrained formulation from the Lagrangian (2.28) we partially fix the gauge invariance as was done in [43][44][45][46][47][48][49][50][51][52] (putting there the curvature to zero, R = 0), except that we will not fix gauge invariance corresponding to the gauge parameter |ε (we remove only the dependence on b…”

“…Our main aim is to derive the gauge invariant Lagrangian using the method of BRST construction [43][44][45][46][47][48][49][50][51][52] in the quadratic approximation in the field strength F μν of the external field. This method in fact yields a gauge invariant Lagrangian description for massive higher spin fields in extended Fock space and therefore the Lagrangian will contain, apart from the basic fields, some additional fields, such as Stückelberg fields.…”

Massive Mixed Symmetry Field Dynamics in Open Bosonic String Theory

“…Therefore a higher spin field theory in higher dimensions should describe a mixed symmetry fields dynamics (see e.g. [3,4,5,6,7,8,9,10,11]). Mixed symmetry fields naturally arise in context of superstring theory (see more about relation the string and the higher spin theories e.g.…”