No abstract

Consistent couplings between a set of vector fields and a system of matter fields are analysed in the framework of Lagrangian BRST cohomology.

Under the hypotheses of smoothness in the coupling constant, locality, Lorentz covariance, and Poincaré invariance of the deformations, combined with the preservation of the number of derivatives on each field, the consistent interactions between a single free massless tensor gauge field with the mixed symmetry of a two-column Young diagram of the type (3,1) and one Abelian vector field have been investigated. The computations are done with the help of the deformation theory based on a cohomological approach, in the context of the antifield-BRST formalism. The main result is that there exist nontrivial cross-couplings between these types of fields in five spatiotemporal dimensions, which break the PT invariance and allow for the deformation of the gauge transformations of the vector field, but not of the gauge algebra.

In this paper we develop an irreducible antifield BRST-anti-BRST formalism for reducible gauge theories. * 359 Int. J. Mod. Phys. A 1999.14:359-386. Downloaded from www.worldscientific.com by UNIVERSITY OF CALIFORNIA @ DAVIS on 02/08/15. For personal use only. Int. J. Mod. Phys. A 1999.14:359-386. Downloaded from www.worldscientific.com by UNIVERSITY OF CALIFORNIA @ DAVIS on 02/08/15. For personal use only.

Consistent interactions that can be added to a free, Abelian gauge theory comprising a finite collection of BF models and a finite set of two-form gauge fields (with the Lagrangian action written in firstorder form as a sum of Abelian Freedman-Townsend models) are constructed from the deformation of the solution to the master equation based on specific cohomological techniques. Under the hypotheses of smoothness in the coupling constant, locality, Lorentz covariance, and Poincaré invariance of the interactions, supplemented with the requirement on the preservation of the number of derivatives on each field with respect to the free theory, we obtain that the deformation procedure modifies the Lagrangian action, the gauge transformations as well as the accompanying algebra. The interacting Lagrangian action contains a generalized version of non-Abelian Freedman-Townsend model. The consistency of interactions to all orders in the coupling constant unfolds certain equations, which are shown to have solutions.