# 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.

## Key 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.