标题： CHL模型中的mock模性 显示英文标题

标题： Mock Modularity In CHL Models

摘要： 达布霍卡尔、穆尔蒂和扎吉尔（DMZ）证明了对于索引为整数且在扭转点处具有极点的亚纯雅可比形式 $\mathrm{SL}(2, \mathbb{Z})$，存在一个标准分解，将其分为极性部分和有限部分，并且表明有限部分是一个虚雅可比形式。本文将DMZ的结果推广到对于共轭子群 $\mathrm{SL}(2, \mathbb{Z})$ 的有理索引的亚纯雅可比形式。作为应用，我们确立了一大类CHL模型中的单中心黑洞退化度由虚雅可比形式的傅里叶系数给出。在这个过程中，我们改进了DMZ关于单中心黑洞退化度由虚模形式表示的电荷集合的结果。特别是，在DMZ研究的情况下，我们给出了单中心退化度不能被预期索引的虚模形式捕捉到的一些电荷例子。 显示英文摘要

摘要： Dabholkar, Murthy and Zagier (DMZ) proved that there is a canonical decomposition of a meromorphic Jacobi form of integral index for $\mathrm{SL}(2, \mathbb{Z})$ with poles on torsion points into polar and finite parts, and showed that the finite part is a mock Jacobi form. In this paper we generalize the results of DMZ to meromorphic Jacobi forms of rational index for congruence subgroups of $\mathrm{SL}(2, \mathbb{Z})$. As an application, we establish that a large class of single-centered black hole degeneracies in CHL models are given by the Fourier coefficients of mock Jacobi forms. In this process we refine the result of DMZ regarding the set of charges for which the single-centered black hole degeneracies are given by a mock modular form. In particular, in the case studied by DMZ, we present examples of charges for which the single-centered degeneracies are not captured by the mock modular form of the expected index.