ZN symmetries, anomalies, and the modular bootstrap

We explore constraints on (1+1)d unitary conformal field theory with an internal ZN global symmetry, by bounding the lightest symmetry-preserving scalar primary operator using the modular bootstrap. Among the other constraints we have found, we prove the existence of a ZN-symmetric relevant/marginal...

Full description

Saved in:
Bibliographic Details
Published in:Physical review. D 2021-06, Vol.103 (12), p.1
Main Authors: Lin, Ying-Hsuan, Shao, Shu-Heng
Format: Article
Language:English
Subjects:
Anomalies
Field theory
Symmetry
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We explore constraints on (1+1)d unitary conformal field theory with an internal ZN global symmetry, by bounding the lightest symmetry-preserving scalar primary operator using the modular bootstrap. Among the other constraints we have found, we prove the existence of a ZN-symmetric relevant/marginal operator if N−1≤c≤9−N for N≤4, with the end points saturated by various Wess-Zumino-Witten models that can be embedded into (e8)1. Its existence implies that robust gapless fixed points are not possible in this range of c if only a ZN symmetry is imposed microscopically. We also obtain stronger, more refined bounds that depend on the 't Hooft anomaly of the ZN symmetry.
ISSN:2470-0010
2470-0029
DOI:10.1103/PhysRevD.103.125001