Scale and conformal invariance in field theory: a physical counterexample

TL;DR

This paper presents a physical example from two-dimensional elasticity theory demonstrating a field theory that exhibits scale invariance without conformal invariance, highlighting a nuanced distinction in symmetry properties.

Contribution

It provides a concrete physical counterexample showing scale invariance without conformal invariance in a well-understood field theory.

Findings

Elasticity theory in 2D exhibits scale but not conformal invariance.

The example clarifies the difference between scale and conformal symmetries.

This challenges assumptions about symmetry implications in field theories.

Abstract

In this note, we illustrate how the two-dimensional theory of elasticity provides a physical example of field theory displaying scale but not conformal invariance.