Weyl Invariance and the Origins of Mass

TL;DR

This paper develops a Weyl invariant framework using tractor calculus to unify massless, massive, and partially massless fields, linking masses to Weyl weights and stability bounds in anti de Sitter space.

Contribution

It introduces a novel tractor calculus approach to maintain Weyl invariance and unify different mass regimes in field theories.

Findings

Masses are related to tractor Weyl weights.

Stability bounds correspond to reality conditions on weights.

Equivalence between tractor and higher spin systems is established.

Abstract

By a uniform and simple Weyl invariant coupling of scale and matter fields, we construct theories that unify massless, massive, and partially massless excitations. Masses are related to tractor Weyl weights, and Breitenlohner-Freedman stability bounds in anti de Sitter amount to reality of these weights. The method relies on tractor calculus -- mathematical machinery allowing Weyl invariance to be kept manifest at all stages. The equivalence between tractor and higher spin systems with arbitrary spins and masses is also considered.