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

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

doi:10.1103/physrevd.93.125025

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

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

Authors

M. Hogevorst

S. Rychkov

B.C. van Rees

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
Related Public URLs	http://arxiv.org/abs/1512.00013

Files

Published Journal Article (353 Kb)
PDF

Copyright Statement
This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published Hogevorst, M., Rychkov, S. & van Rees, B.C. (2016). Unitarity violation at the Wilson-Fisher fixed point in 4-epsilon dimensions. Physical Review D 93: 125025, https://doi.org/10.1103/PhysRevD.93.125025