Dual linearized gravity in D=6 coupled to a purely spin-two field of mixed symmetry (2,2)

TL;DR

This paper explores consistent interactions between specific mixed symmetry tensor fields in six-dimensional linearized gravity, revealing how dual gravity couples to a spin-two field without altering the gauge algebra.

Contribution

It demonstrates the first consistent coupling of dual linearized gravity in D=6 to a purely spin-two mixed symmetry field using a cohomological deformation approach.

Findings

Coupling modifies gauge transformations and reducibility relations.

Gauge algebra remains unchanged.

Provides a cohomological framework for mixed symmetry field interactions.

Abstract

Under the hypotheses of analyticity, locality, Lorentz covariance, and Poincare invariance of the deformations, combined with the requirement that the interaction vertices contain at most two spatiotemporal derivatives of the fields, we investigate the consistent interactions between a single massless tensor field with the mixed symmetry (3,1) and one massless tensor field with the mixed symmetry (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 result is that dual linearized gravity in D=6 gets coupled to a purely spin-two field with the mixed symmetry of the Riemann tensor such that both the gauge transformations and first-order reducibility relations in the (3,1) sector are changed, but not the gauge algebra.