Selfinteractions in collections of massless tensor fields with the mixed symmetry (3,1) and (2,2)

TL;DR

This paper investigates the possibility of adding consistent selfinteractions to collections of massless tensor fields with mixed symmetry, using a cohomological approach within the antifield-BRST formalism, and finds no nontrivial gauge-deforming interactions.

Contribution

It provides a cohomological analysis showing that no gauge-deforming selfinteractions are possible for these tensor fields under specified conditions.

Findings

No selfinteractions deforming gauge transformations are found.

Cosmological terms can be added for (2,2) tensor fields.

The analysis uses antifield-BRST and deformation theory methods.

Abstract

Under the hypotheses of analyticity, locality, Lorentz covariance, and Poincare invariance of the deformations, combined with the requirement that the interaction vertices contain at most two spatiotemporal derivatives of the fields, we investigate the consistent selfinteractions that can be added to a collection of massless tensor fields with the mixed symmetry (3,1) and respectively (2,2). The computations are done with the help of the deformation theory based on a cohomological approach, in the context of the antifield-BRST formalism. Our result is that no selfinteractions that deform the original gauge transformations emerge. In the case of the collection of (2,2) tensor fields it is possible to add a sum of cosmological terms to the free Lagrangian.