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

Abstract

Non-trivial, consistent interactions of a free, massless tensor field t_{μν|αβ} 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 Poincaré 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.

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

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• On electromagnetic interactions for massive mixed symmetry field
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• Consistent interactions of dual linearized gravity in D=5: couplings with a topological BF model
• Interactions between a massless tensor field with the mixed symmetry of the Riemann tensor and a massless vector field
• Lovelock Terms and BRST Cohomology
• Dual linearized gravity in D=6 coupled to a purely spin-two field of mixed symmetry (2,2)
• No cross-interactions between the Weyl graviton and the massless Rarita-Schwinger field
• Yes-go cross-couplings in collections of tensor fields with mixed symmetries of the type (3,1) and (2,2)