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$\mathbb{Z}_N$ Symmetries, Anomalies, and the Modular Bootstrap

Authors :
Lin, Ying-Hsuan
Shao, Shu-Heng
Source :
Phys. Rev. D 103, 125001 (2021)
Publication Year :
2021

Abstract

We explore constraints on (1+1)$d$ unitary conformal field theory with an internal $\mathbb{Z}_N$ 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 $\mathbb{Z}_N$-symmetric relevant/marginal operator if $N-1 \le c\le 9-N$ for $N\leq4$, with the endpoints saturated by various WZW models that can be embedded into $(\mathfrak{e}_8)_1$. Its existence implies that robust gapless fixed points are not possible in this range of $c$ if only a $\mathbb{Z}_N$ symmetry is imposed microscopically. We also obtain stronger, more refined bounds that depend on the 't Hooft anomaly of the $\mathbb{Z}_N$ symmetry.<br />Comment: 26+13 pages, 10 figures, 2 tables; v2: minor revision

Details

Database :
arXiv
Journal :
Phys. Rev. D 103, 125001 (2021)
Publication Type :
Report
Accession number :
edsarx.2101.08343
Document Type :
Working Paper
Full Text :
https://doi.org/10.1103/PhysRevD.103.125001