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$\mathbb{Z}_N$ Symmetries, Anomalies, and the Modular Bootstrap
- 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
- Subjects :
- High Energy Physics - Theory
Condensed Matter - Strongly Correlated Electrons
Subjects
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