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arXiv · 2101.08343

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

Ying-Hsuan Lin·Shu-Heng Shao
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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.

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Ying-Hsuan Lin, Shu-Heng Shao. 2021-01-20. $\mathbb{Z}_N$ Symmetries, Anomalies, and the Modular Bootstrap. https://doi.org/10.1103/physrevd.103.125001

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