Weyl versus conformal invariance in quantum field theory

• Main Authors: Kara Farnsworth, Markus A. Luty, Valentina Prilepina
• Format: Article
• Language: English
• Published: SpringerOpen 2017-10-01
• Series: Journal of High Energy Physics
• Subjects: Conformal Field Theory; Effective Field Theories; Space-Time Symmetries
• Online Access: http://link.springer.com/article/10.1007/JHEP10(2017)170

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 ≤ 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.