BRST cohomological results on the massless tensor field with the mixed symmetry of the Riemann tensor

The basic BRST cohomological properties of a free, massless tensor field with the mixed symmetry of the Riemann tensor are studied in detail. It is shown that any non-trivial co-cycle from the local BRST cohomology group can be taken to stop at antighost number three, its last component belonging to the cohomology of the exterior longitudinal derivative and containing non-trivial elements from the (invariant) characteristic cohomology.Comment: 39 page

Interactions of a massless tensor field with the mixed symmetry of the Riemann tensor. No-go results

Non-trivial, consistent interactions of a free, massless tensor field t_{\mu \nu |\alpha \beta} with the mixed symmetry of the Riemann tensor are studied in the following cases: self-couplings, cross-interactions with a Pauli-Fierz field and cross-couplings with purely matter theories. The main results, obtained from BRST cohomological techniques under the assumptions on smoothness, locality, Lorentz covariance and Poincar\'{e} invariance of the deformations, combined with the requirement that the interacting Lagrangian is at most second-order derivative, can be synthesized into: no consistent self-couplings exist, but a cosmological-like term; no cross-interactions with the Pauli-Fierz field can be added; no non-trivial consistent cross-couplings with the matter theories such that the matter fields gain gauge transformations are allowed.Comment: for version 3: 45 pages, uses amssymb; shortened version, the three appendices from version 2 can be found in hep-th/040209

Two-dimensional interactions between a BF-type theory and a collection of vector fields

Consistent interactions that can be added to a two-dimensional, free abelian gauge theory comprising a special class of BF-type models and a collection of vector fields are constructed from the deformation of the solution to the master equation based on specific cohomological techniques. The deformation procedure modifies the Lagrangian action, the gauge transformations, as well as the accompanying algebra of the interacting model.Comment: LaTeX 2e, 31 page

On the generalized Freedman-Townsend model

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 first-order 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 Poincare 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.Comment: LaTeX, 62 page

Consistent interactions of dual linearized gravity in D=5: couplings with a topological BF model

Under some plausible assumptions, we find that the dual formulation of linearized gravity in D=5 can be nontrivially coupled to the topological BF model in such a way that the interacting theory exhibits a deformed gauge algebra and some deformed, on-shell reducibility relations. Moreover, the tensor field with the mixed symmetry (2,1) gains some shift gauge transformations with parameters from the BF sector.Comment: 63 pages, accepted for publication in Eur. Phys. J.

Four-dimensional couplings among BF and massless Rarita-Schwinger theories: a BRST cohomological approach

The local and manifestly covariant Lagrangian interactions in four spacetime dimensions that can be added to a free model that describes a massless Rarita-Schwinger theory and an Abelian BF theory are constructed by means of deforming the solution to the master equation on behalf of specific cohomological techniques.Comment: 59 page