Unitarity violation at the Wilson-Fisher fixed point in 4-epsilon dimensions

Hogevorst, M.; Rychkov, S.; van Rees, B.C.

Abstract

We consider the continuation of free and interacting scalar field theory to noninteger spacetime dimension d. We find that the correlation functions in these theories are necessarily incompatible with unitarity (or with reflection positivity in Euclidean signature). In particular, the theories contain negative-norm states unless d is a positive integer. These negative-norm states can be obtained via the operator product expansion from simple positive-norm operators, and are therefore an integral part of the theory. At the Wilson-Fisher fixed point the nonunitarity leads to the existence of complex anomalous dimensions. We demonstrate that they appear already at leading order in the epsilon expansion.

Citation

Hogevorst, M., Rychkov, S., & van Rees, B. (2016). Unitarity violation at the Wilson-Fisher fixed point in 4-epsilon dimensions. Physical Review D, 93(12), Article 125025. https://doi.org/10.1103/physrevd.93.125025

• Journal Article Type: Article
• Acceptance Date: Dec 14, 2015
• Online Publication Date: Jun 20, 2016
• Publication Date: Jun 20, 2016
• Deposit Date: Dec 30, 2015
• Publicly Available Date: Dec 14, 2016
• Journal: Physical Review D
• Print ISSN: 2470-0010
• Electronic ISSN: 2470-0029
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 93
• Issue: 12
• Article Number: 125025
• DOI: https://doi.org/10.1103/physrevd.93.125025
• Public URL: https://durham-repository.worktribe.com/output/1395850
• Related Public URLs: http://arxiv.org/abs/1512.00013