Twenty years of the Weyl anomaly

1993/08/16 by M. J. Duff, M J Duff · 598 citations
Physics and Astronomy · #Anomaly (physics) #Black Holes and Theoretical Physics #Conformal anomaly #Conformal gravity #Conformal map #Massless particle #Metric (unit) #Noncommutative and Quantum Gravity Theories #Quantum and Classical Electrodynamics #String (physics) #String theory #Weyl transformation #gr-qc #hep-th

paper · pdf · doi:10.1088/0264-9381/11/6/004

published in Classical and Quantum Gravity 11(6), 1387-1403 (IOP Publishing) · 43 pages

arxiv created 1993/08/16 · openalex publication_date 1994/06/01 · arxiv updated 2010/04/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/08

Abstract

In 1973 two Salam protégés (Derek Capper and the author) discovered that the conformal invariance under Weyl rescalings of the metric tensor 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.

Citations

• Is there a c-theorem in four dimensions?
• Quantum Gravity and World Topology
• Moduli corrections to gravitational couplings from string loops
• Analogs of the c-theorem for four-dimensional renormalisable field theories
• Quantum geometry of bosonic strings
• Zeta function regularization of path integrals in curved spacetime
• Regularization and renormalization of gauge fields
• Quantum field theory in de Sitter space: renormalization by point-splitting
• Supermembranes and eleven-dimensional supergravity
• Dimensional renorinalization : The number of dimensions as a regularizing parameter
• Reine Infinitesimalgeometrie
• Heterotic solitons

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