Conformal Invariance for a Class of Scale Invariant Theories in Four Dimensions

TL;DR

This paper demonstrates that in four-dimensional, unitary, scale-invariant quantum field theories without higher derivatives, scale invariance necessarily implies conformal invariance, using the Wess-Zumino consistency condition for the Weyl anomaly.

Contribution

It provides a proof that scale invariance leads to conformal invariance in a specific class of four-dimensional quantum field theories.

Findings

Scale invariance implies conformal invariance under given conditions.

The proof uses the Wess-Zumino consistency condition for the Weyl anomaly.

The result applies to theories without higher derivatives and with a well-defined scale current.

Abstract

For a four dimensional, unitary, diffeomorphism- and scale invariant quantum field theory without higher derivatives and a well defined scale current we argue that scale invariance implies conformal invariance. The proof relies on the Wess-Zumino consistency condition for the Weyl anomaly.