Weyl versus conformal invariance in quantum field theory

DOI10.1007/JHEP10(2017)170zbMATH Open1383.81209arXiv1702.07079OpenAlexW2603928152MaRDI QIDQ1709375

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Publication date: 27 March 2018

Published in: (Search for Journal in Brave)

Abstract: We argue that conformal invariance in flat spacetime implies Weyl invariance in a general curved background metric for all unitary theories in spacetime dimensions $dleq10$. We also study possible curvature corrections to the Weyl transformations of operators, and show that these are absent for operators of sufficiently low dimensionality and spin. We find possible `anomalous' Weyl transformations proportional to the Weyl (Cotton) tensor for $d>3$ ($d=3$). The arguments are based on algebraic consistency conditions similar to the Wess-Zumino consistency conditions that classify possible local anomalies. The arguments can be straightforwardly extended to larger operator dimensions and higher $d$ with additional algebraic complexity.

Full work available at URL: https://arxiv.org/abs/1702.07079

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