Weyl invariance with a nontrivial mass scale

TL;DR

This paper introduces a Weyl-invariant theory that incorporates a nontrivial mass scale, which is only invariant under transverse diffeomorphisms, leading to unique implications for scale invariance in free-falling frames.

Contribution

It presents a novel Weyl-invariant theory with a nontrivial mass scale that is only invariant under transverse diffeomorphisms, challenging traditional notions of scale invariance.

Findings

Weyl invariance does not imply scale invariance in free-falling frames.

The theory is invariant under a restricted class of diffeomorphisms.

Physical implications of the nontrivial mass scale are discussed.

Abstract

A theory with a mass scale and yet Weyl invariant is presented. The theory is not invariant under all diffeomorphisms but only under transverse ones. This is the reason why Weyl invariance does not imply scale invariance in a free falling frame. Physical implications of this framework are discussed.