Moonshine, superconformal symmetry, and quantum error correction

Harvey, Jeffrey A.; Moore, Gregory W.

doi:10.1007/jhep05(2020)146

Title: Moonshine, superconformal symmetry, and quantum error correction

Journal Article · Wed May 27 00:00:00 EDT 2020 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep05(2020)146· OSTI ID:1802014

^[1]; Moore, Gregory W. ^[2]

Univ. of Chicago, IL (United States). Enrico Fermi Inst.
Rutgers Univ., Piscataway, NJ (United States). Dept. of Physics and Astronomy. NHETC

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).

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Research Organization:: Rutgers Univ., Piscataway, NJ (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0010008

OSTI ID:: 1802014

Journal Information:: Journal of High Energy Physics (Online), Vol. 2020, Issue 5; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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