ar X iv : h ep - t h / 93 08 07 5 v 1 1 6 A ug 1 99 3 CTP - TAMU - 06 / 93 Twenty Years of the Weyl Anomaly †

In 1973 two Salam protégés (Derek Capper and the author) discovered that the conformal invariance under Weyl rescalings of the metric tensor gμν(x) → Ω(x)gμν(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. CTP/TAMU-06/93 July 1993 Talk given at the Salamfest, ICTP, Trieste, March 1993. ‡ Research supported in part by NSF Grant PHY-9106593. When all else fails, you can always tell the truth. Abdus Salam 1 Trieste and Oxford Twenty years ago, Derek Capper and I had embarked on our very first postdocs here in Trieste. We were two Salam students fresh from Imperial College filled with ideas about quantizing the gravitational field: a subject which at the time was pursued only by mad dogs and Englishmen. (My thesis title: Problems in the Classical and Quantum Theories of Gravitation was greeted with hoots of derision when I announced it at the Cargese Summer School en route to Trieste. The work originated with a bet between Abdus Salam and Hermann Bondi about whether you could generate the Schwarzschild solution using Feynman diagrams. You can (and I did) but I never found out if Bondi ever paid up.) Inspired by Salam, Capper and I decided to use the recently discovered dimensional regularization to calculate corrections to the graviton propagator from closed loops of massless particles: vectors [1] and spinors [2], the former in collaboration with Leopold Halpern. This involved the self-energy Dimensional regularization had just been invented by another Salam student and contempory of ours, Jonathan Ashmore [3], and independently by Bollini and Giambiagi [4] and by ’t Hooft and Veltman [5]. I briefly shared a London house with Jonathan Ashmore and Fritjof Capra. Both were later to leave physics, as indeed was Derek Capper. Ashmore went into biology, Capper into computer science and Capra into eastern mysticism (a decision in which, as far as I am aware, Abdus Salam played no part).