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

Physics – High Energy Physics – High Energy Physics - Theory

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for version 3: 45 pages, uses amssymb; shortened version, the three appendices from version 2 can be found in hep-th/0402099

Scientific paper

10.1140/epjc/s2004-01888-y

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.

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