Interactions between a massless tensor field with the mixed symmetry of the Riemann tensor and a massless vector field

TL;DR

This paper proves that under certain physical and mathematical assumptions, there are no consistent interactions between a specific type of massless tensor field with Riemann tensor symmetry and a massless vector field.

Contribution

The study demonstrates, using BRST cohomology, that no cross-interactions are possible between these fields under the specified conditions.

Findings

No consistent cross-interactions found

Results are based on BRST cohomology analysis

Assumptions include smoothness, locality, Lorentz covariance, and second-order derivatives

Abstract

Consistent couplings between a massless tensor field with the mixed symmetry of the Riemann tensor and a massless vector field are analyzed in the framework of Lagrangian BRST cohomology. Under the assumptions on smoothness, locality, Lorentz covariance, and Poincare invariance of the deformations, combined with the requirement that the interacting Lagrangian is at most second-order derivative, it is proved that there are no consistent cross-interactions between a single massless tensor field with the mixed symmetry of the Riemann tensor and one massless vector field.