Weyl versus Conformal Invariance in Quantum Field Theory

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 $d\le 10$. 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.

30 pages, v3: Version accepted to JHEP, clarifications added and typos fixed

References in corpus (3)

• Restricted Weyl invariance in four-dimensional curved spacetime
• Critical behavior of the Ising model with long range interactions
• Unitarity, Locality, and Scale versus Conformal Invariance in Four Dimensions

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