Inertial Symmetry Breaking

TL;DR

This paper discusses how Weyl invariant theories can undergo inertial symmetry breaking without relying on potentials, using current algebra and renormalization conditions to maintain invariance at the quantum level.

Contribution

It introduces a framework for inertial symmetry breaking in Weyl invariant theories and demonstrates how to preserve Weyl invariance through specific renormalization conditions.

Findings

Weyl invariance can be broken inertially without potentials

A Weyl invariant Coleman-Weinberg potential is computed

Scale and U(1) symmetry breaking are achieved simultaneously

Abstract

We review and expand upon recent work demonstrating that Weyl invariant theories can be broken "inertially," which does not depend upon a potential. This can be understood in a general way by the "current algebra" of these theories, independently of specific Lagrangians. Maintaining the exact Weyl invariance in a renormalized quantum theory can be accomplished by renormalization conditions that refer back to the VEV's of fields in the action. We illustrate the computation of a Weyl invariant Coleman-Weinberg potential that breaks a U(1) symmetry together,with scale invariance.