Twenty Years of the Weyl Anomaly

TL;DR

This paper reviews twenty years of research on the Weyl anomaly, highlighting its discovery, significance, and applications across various fields like black hole physics, cosmology, string theory, and statistical mechanics.

Contribution

It provides a comprehensive historical overview of Weyl anomalies, emphasizing their development and impact in theoretical physics over two decades.

Findings

Weyl anomalies break classical conformal invariance at the quantum level.

Applications of Weyl anomalies span black hole physics, cosmology, string theory, and statistical mechanics.

The review reflects on the historical and scientific significance of Weyl anomalies.

Abstract

In 1973 two Salam prot\'{e}g\'{e}s (Derek Capper and the author) discovered that the conformal invariance under Weyl rescalings of the metric tensor $g_{\mu\nu}(x)\rightarrow\Omega^2(x)g_{\mu\nu}(x)$ displayed by classical massless field systems in interaction with gravity no longer survives in the quantum theory. Since then these Weyl anomalies have found a variety of applications in black hole physics, cosmology, string theory and statistical mechanics. We give a nostalgic review. (Talk given at the {\it Salamfest}, ICTP, Trieste, March 1993.)