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Title: Moonshine, superconformal symmetry, and quantum error correction

Abstract

Special conformal field theories can have symmetry groups which are interesting sporadic finite simple groups. Famous examples include the Monster symmetry group of a c = 24 twodimensional conformal field theory (CFT) constructed by Frenkel, Lepowsky and Meurman, and the Conway symmetry group of a c = 12 CFT explored in detail by Duncan and Mack-Crane. The Mathieu moonshine connection between the K3 elliptic genus and the Mathieu group M24 has led to the study of K3 sigma models with large symmetry groups. A particular K3 CFT with a maximal symmetry group preserving (4, 4) superconformal symmetry was studied in beautiful work by Gaberdiel, Taormina, Volpato, and Wendland [41]. The present paper shows that in both the GTVW and c = 12 theories the construction of superconformal generators can be understood via the theory of quantum error correcting codes. The automorphism groups of these codes lift to symmetry groups in the CFT preserving the superconformal generators. In the case of the N = 1 supercurrent of the GTVW model our result, combined with a result of T. Johnson-Freyd implies the symmetry group is the maximal subgroup of M24 known as the sextet group. (The sextet group is also known asmore » the holomorph of the hexacode.) Building on [41] the Ramond-Ramond sector of the GTVW model is related to the Miracle Octad Generator which in turn leads to a role for the Golay code as a group of symmetries of RR states. Moreover, (4, 1) superconformal symmetry suffices to define and decompose the elliptic genus of a K3 sigma model into characters of the N = 4 superconformal algebra. The symmetry group preserving (4, 1) is larger than that preserving (4, 4).« less

Authors:
ORCiD logo [1];  [2]
  1. Univ. of Chicago, IL (United States). Enrico Fermi Inst.
  2. Rutgers Univ., Piscataway, NJ (United States). Dept. of Physics and Astronomy. NHETC
Publication Date:
Research Org.:
Rutgers Univ., Piscataway, NJ (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1802014
Grant/Contract Number:  
SC0010008
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2020; Journal Issue: 5; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Physics

Citation Formats

Harvey, Jeffrey A., and Moore, Gregory W. Moonshine, superconformal symmetry, and quantum error correction. United States: N. p., 2020. Web. doi:10.1007/jhep05(2020)146.
Harvey, Jeffrey A., & Moore, Gregory W. Moonshine, superconformal symmetry, and quantum error correction. United States. https://doi.org/10.1007/jhep05(2020)146
Harvey, Jeffrey A., and Moore, Gregory W. Wed . "Moonshine, superconformal symmetry, and quantum error correction". United States. https://doi.org/10.1007/jhep05(2020)146. https://www.osti.gov/servlets/purl/1802014.
@article{osti_1802014,
title = {Moonshine, superconformal symmetry, and quantum error correction},
author = {Harvey, Jeffrey A. and Moore, Gregory W.},
abstractNote = {Special conformal field theories can have symmetry groups which are interesting sporadic finite simple groups. Famous examples include the Monster symmetry group of a c = 24 twodimensional conformal field theory (CFT) constructed by Frenkel, Lepowsky and Meurman, and the Conway symmetry group of a c = 12 CFT explored in detail by Duncan and Mack-Crane. The Mathieu moonshine connection between the K3 elliptic genus and the Mathieu group M24 has led to the study of K3 sigma models with large symmetry groups. A particular K3 CFT with a maximal symmetry group preserving (4, 4) superconformal symmetry was studied in beautiful work by Gaberdiel, Taormina, Volpato, and Wendland [41]. The present paper shows that in both the GTVW and c = 12 theories the construction of superconformal generators can be understood via the theory of quantum error correcting codes. The automorphism groups of these codes lift to symmetry groups in the CFT preserving the superconformal generators. In the case of the N = 1 supercurrent of the GTVW model our result, combined with a result of T. Johnson-Freyd implies the symmetry group is the maximal subgroup of M24 known as the sextet group. (The sextet group is also known as the holomorph of the hexacode.) Building on [41] the Ramond-Ramond sector of the GTVW model is related to the Miracle Octad Generator which in turn leads to a role for the Golay code as a group of symmetries of RR states. Moreover, (4, 1) superconformal symmetry suffices to define and decompose the elliptic genus of a K3 sigma model into characters of the N = 4 superconformal algebra. The symmetry group preserving (4, 1) is larger than that preserving (4, 4).},
doi = {10.1007/jhep05(2020)146},
journal = {Journal of High Energy Physics (Online)},
number = 5,
volume = 2020,
place = {United States},
year = {Wed May 27 00:00:00 EDT 2020},
month = {Wed May 27 00:00:00 EDT 2020}
}

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