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Z_N Symmetries, Anomalies, and the Modular Bootstrap

Lin, Ying-Hsuan and Shao, Shu-Heng (2021) Z_N Symmetries, Anomalies, and the Modular Bootstrap. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20210122-075637022

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Abstract

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 endpoints saturated by various WZW 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.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/2101.08343arXivDiscussion Paper
ORCID:
AuthorORCID
Lin, Ying-Hsuan0000-0001-8904-1287
Shao, Shu-Heng0000-0003-1294-2786
Additional Information:We thank Luca Delacrétaz, Meng Cheng, Pranay Gorantla, Theo Johnson-Freyd, Zohar Komargodski, Ho Tat Lam, Michael Levin, Kantaro Ohmori, and Nathan Seiberg for helpful discussions. We are grateful to Meng Cheng, Theo Johnson-Freyd, and Justin Kulp for comments on the first draft. YL is supported by the Sherman Fairchild Foundation, by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632, and by the Simons Collaboration Grant on the Non-Perturbative Bootstrap. SHS is supported by the Simons Collaboration on Ultra-Quantum Matter, which is a grant from the Simons Foundation (651440, NS). This research was supported in part by the National Science Foundation under Grant No. NSF PHY-1748958.
Group:Walter Burke Institute for Theoretical Physics
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Sherman Fairchild FoundationUNSPECIFIED
Simons Foundation651440
NSFPHY-1748958
Other Numbering System:
Other Numbering System NameOther Numbering System ID
CALT-TH2021-002
Record Number:CaltechAUTHORS:20210122-075637022
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210122-075637022
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:107651
Collection:CaltechAUTHORS
Deposited By: Joy Painter
Deposited On:22 Jan 2021 18:25
Last Modified:22 Jan 2021 18:26

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