Conformal Field Theories with Sporadic Group Symmetry
Conformal Field Theories with Sporadic Group Symmetry
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DOI：
10.1007/s00220-021-04207-7
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发表时间：
2020-02
影响因子：
2.4
通讯作者：
J. Bae;J. Harvey;Kimyeong Lee;Sungjay Lee;Brandon C. Rayhaun
中科院分区：
文献类型：
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作者：
J. Bae;J. Harvey;Kimyeong Lee;Sungjay Lee;Brandon C. Rayhaun
怪物偶发群是中心荷顶点算子代数（VOA）或亚纯共形场论（CFT）的自同构群。除了它的应力张量T（z）之外，这个理论还包含许多其他较小中心电荷的共形向量;例如，它允许48个和为T（z）的共形向量。这种分解的应力张量允许一个新的CFTs从怪物CFT的方式类似于戈达德-肯特-橄榄（GKO）陪集方法仿射李代数。我们使用这个过程中产生的证据存在的一些CFTs与零星的对称群，并采用各种技术，包括Hecke运营商，模块化线性微分方程，和Rademacher总和，计算这些CFTs的字符。我们的例子包括九个零星的群作为怪物的子群出现，以及简单的群和李型。这些例子中的许多都与McKay的对应关系有关，我们更普遍地使用Norton的monstralizer对的结构来组织我们的演示。
The monster sporadic group is the automorphism group of a central chargevertex operator algebra (VOA) or meromorphic conformal field theory (CFT). In addition to itsstress tensorT(z), this theory contains many other conformal vectors of smaller central charge; for example, it admits 48 commutingconformal vectors whose sum isT(z). Such decompositions of the stress tensor allow one to construct new CFTs from the monster CFT in a manner analogous to the Goddard-Kent-Olive (GKO) coset method for affine Lie algebras. We use this procedure to produce evidence for the existence of a number of CFTs with sporadic symmetry groups and employ a variety of techniques, including Hecke operators, modular linear differential equations, and Rademacher sums, to compute the characters of these CFTs. Our examples include (extensions of) nine of the sporadic groups appearing as subquotients of the monster, as well as the simple groupsandof Lie type. Many of these examples are naturally associated to McKay’scorrespondence, and we use the structure of Norton’s monstralizer pairs more generally to organize our presentation.