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Yes-go cross-couplings in collections of tensor fields with mixed symmetries of the type (3,1) and (2,2). (English) Zbl 1188.81152

Summary: Under the hypotheses of analyticity, locality, Lorentz covariance, and Poincaré invariance of the deformations, combined with the requirement that the interaction vertices contain at most two space-time derivatives of the fields, we investigate the consistent cross-couplings between two collections of tensor fields with the mixed symmetries of the type (3,1) and (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 results can be synthesized in: (i) there appear consistent cross-couplings between the two types of field collections at order one and two in the coupling constant such that some of the gauge generators and of the reducibility functions are deformed, and (ii) the existence or not of cross-couplings among different fields with the mixed symmetry of the Riemann tensor depends on the indefinite or respectively positive-definite behavior of the quadratic form defined by the kinetic terms from the free Lagrangian.

MSC:

81T70 Quantization in field theory; cohomological methods
14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)
53D45 Gromov-Witten invariants, quantum cohomology, Frobenius manifolds
58D30 Applications of manifolds of mappings to the sciences
81Q30 Feynman integrals and graphs; applications of algebraic topology and algebraic geometry
83C45 Quantization of the gravitational field
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