Moonshine, superconformal symmetry, and quantum error correction
Moonshine, superconformal symmetry, and quantum error correction
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Moonshine、超共形对称性和量子纠错
DOI：
10.1007/jhep05(2020)146
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发表时间：
2020
影响因子：
5.4
通讯作者：
Moore, Gregory W.
中科院分区：
文献类型：
--
作者：
Harvey, Jeffrey A.;Moore, Gregory W.
特殊的共形场论可以有对称群，对称群是有趣的零星有限单群。著名的例子包括由Frenkel，Lepowsky和Meurman构造的c=24二维共形场论(CFT)的Monster对称群，以及Duncan和Mack-Crane详细研究的c=12二维共形场论的Conway对称群。K3椭圆亏格与Mathieu群M24之间的Mathieu月光联系导致了具有大对称群的K3 sigma模型的研究。Gaberdiel，Taormina，Volpato和Wendland[41]在漂亮的工作中研究了具有最大对称群保持(4，4)超共形对称性的特殊K3CFT。本文指出，在GTVW理论和c=12理论中，超共形生成元的构造都可以用量子纠错码理论来理解。这些码的自同构群提升为保持超共形生成元的CFT中的对称群。在GTVW模型的N=1超流的情况下，我们的结果与T.Johnson-Freyd的结果相结合，表明对称群是M24的最大子群，称为六重群。(六重群也称为六重全息。)在[41]的基础上，GTVW模型的Ramond-Ramond扇区与奇迹八倍生成器相关，这反过来又导致Golay码作为一组RR态的对称性。此外，(4，1)超共形对称性足以定义和分解K3sigma模型的椭圆亏格为N=4超共形代数的特征标。保持对称群(4，1)大于保持对称群(4，4)。
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 two-dimensional 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 M 24 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 M 24 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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代数、BPS 状态和字符串
DOI：
--
发表时间：
1995
期刊：
影响因子：
--
作者：
J. A. Harvey;G. Moore
通讯作者：
G. Moore
K3 椭圆属中的 Mathieu Moonshine
影响因子：
5.4
作者：
M. Gaberdiel;S. Hohenegger;R. Volpato
通讯作者：
R. Volpato
K3 表面、N=4 Dyons 和 Mathieu 群 M24
DOI：
10.4310/cntp.2010.v4.n4.a2
发表时间：
2010
期刊：
arXiv: High Energy Physics - Theory
影响因子：
--
作者：
Miranda C. N. Cheng
通讯作者：
Miranda C. N. Cheng
本影月光和尼迈尔晶格
影响因子：
1.2
作者：
Miranda C. N. Cheng;John FR Duncan;Jeffrey A. Harvey
通讯作者：
Jeffrey A. Harvey
所有 (4,1)：具有 (4, q) 离壳超对称性的 Sigma 模型
影响因子：
5.4
作者：
C. Hull;U. Lindström
通讯作者：
U. Lindström