Conservation Law for Massive Scale-Invariant Photons in Weyl-Invariant Gravity

TL;DR

This paper demonstrates a gauge theory coupled with scalar-tensor gravity that exhibits Weyl invariance, revealing how scale invariance breaking causes spontaneous gauge symmetry breaking, with implications for massive photons in gravity.

Contribution

It introduces a Weyl-invariant extension of Stueckelberg gauge theory coupled to scalar-tensor gravity, highlighting the role of scale invariance and its breaking in gauge symmetry.

Findings

Weyl symmetry is genuine and non-vanishing in the coupled theory.

Broken scale invariance leads to spontaneous gauge symmetry breaking.

The theory manifests differently in Jordan and Einstein frames.

Abstract

It is demonstrated that a Stueckelberg-type gauge theory, coupled to the scalar-tensor theory of gravity, is invariant under both gauge and Weyl transformations. Unlike the pure Stueckelberg theory, this coupled Lagrangian has a genuine Weyl symmetry, with a non-vanishing current. The above is true in the Jordan frame, whereas in the Einstein frame, the same theory manifests as Proca theory in presence of pure gravity. It is found that broken scale invariance leads to simultaneous spontaneous breaking of the gauge symmetry.