Riemann-Einstein Structure from Volume and Gauge Symmetry

TL;DR

This paper demonstrates how a metric structure can emerge from gauge symmetry and volume considerations through spontaneous symmetry breaking, proposing a polynomial action that includes matter coupling.

Contribution

It introduces a novel approach to induce metric structure from gauge symmetry and volume, with a polynomial action for the symmetric phase.

Findings

Metric structure can be induced from gauge symmetry and volume.

A polynomial action including matter coupling is constructed.

Assuming a preferred volume minimally modifies metric theories.

Abstract

It is shown how a metric structure can be induced in a simple way starting with a gauge structure and a preferred volume, by spontaneous symmetry breaking. A polynomial action, including coupling to matter, is constructed for the symmetric phase. It is argued that assuming a preferred volume, in the context of a metric theory, induces only a limited modification of the theory.