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arXiv 1503.06983hep-thmath-phmath.AGmath.MP
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M弦、单极弦与模形式

M String, Monopole String and Modular Forms

Stefan Hohenegger, Amer Iqbal, Soo-Jong Rey

摘要:

我们研究了六维M弦(M2-膜和M5-膜的一维交叉)和五维M弦(磁荷弦)之间的关系。对于特定的构型,我们提出M弦BPS束缚态的计数函数可以捕获M弦模空间的椭圆亏格。我们检查这个建议的已知情况下,陶布-NUT和Atiyah-Hitchin空间,我们发现完全一致。此外,我们分析了M弦自由能的模性质,它在SL(2,Z)下不协变变换。然而,对于一个给定数量的M-弦,我们发现存在一个唯一的组合的未加细亏格零自由能,转换为一个雅可比形式下的一个同余子群SL(2,Z)。这些组合对应于不同数量的M5-膜的求和,并且只有当它们之间的距离都相等时才有意义。我们解释说,这是一个必要条件的m-弦模空间可分解成相对和质心部分。

英文摘要:

We study relations between M-strings (one-dimensional intersections of M2-branes and M5-branes) in six dimensions and m-strings (magnetically charged monopole strings) in five dimensions. For specific configurations, we propose that the counting functions of BPS bound-states of M-strings capture the elliptic genus of the moduli space of m-strings. We check this proposal for the known cases, the Taub-NUT and Atiyah-Hitchin spaces for which we find complete agreement. Furthermore, we analyze the modular properties of the M-string free energies, which do not transform covariantly under SL(2,Z). However, for a given number of M-strings, we find that there exists a unique combination of unrefined genus-zero free energies that transforms as a Jacobi form under a congruence subgroup of SL(2,Z). These combinations correspond to summing over different numbers of M5-branes and make sense only if the distances between them are all equal. We explain that this is a necessary condition for the m-string moduli space to be factorizable into relative and center-of-mass parts.

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