No interactions for a collection of Weyl gravitons intermediated by a scalar field

TL;DR

This paper proves that, under specific physical and mathematical assumptions, different Weyl gravitons cannot have consistent cross-interactions mediated by a scalar field, highlighting limitations in their possible couplings.

Contribution

The study demonstrates the absence of cross-interactions among multiple Weyl gravitons in the presence of a scalar field using BRST cohomology methods under certain assumptions.

Findings

No consistent cross-interactions among Weyl gravitons with scalar field.

Couplings of a single Weyl graviton to a scalar field are possible.

Results depend on assumptions like locality, Lorentz invariance, and positive definiteness.

Abstract

The cross-couplings among several Weyl gravitons (described in the free limit by a sum of linearized Weyl actions) in the presence of a scalar field are studied with the help of the deformation theory based on local BRST cohomology. Under the hypotheses of locality, smoothness of the interactions in the coupling constant, Poincare invariance, (background) Lorentz invariance, and the preservation of the number of derivatives on each field, together with the supplementary assumption that the internal metric defined by the sum of Weyl lagrangians is positively defined, we prove that there are no consistent cross-interactions among different Weyl gravitons in the presence of a scalar field. The couplings of a single Weyl graviton to a scalar field are also discussed.