计数吸引子背景的不定theta函数
Indefinite theta functions for counting attractor backgrounds
摘要：
本文利用不定θ函数正则化了单中心双子BPS黑洞的正则配分函数。这些配分函数计算四维超环面紧化杂化弦论的希尔伯特空间中的双子简并，由电荷和磁荷分级。正则化是通过将简并度的加权和视为任意选择的黑洞背景的近视界吸引子几何中的电荷激发之和并消除不稳定模式来实现的。这使我们能够重写这些总和的不确定theta函数。背景独立性，然后通过使用椭圆变换下的不定theta函数的变换性质来实现，而模块化的变换是用来接触超引力中的半经典结果。
英文摘要：
In this note, we employ indefinite theta functions to regularize canonical partition functions for single-center dyonic BPS black holes. These partition functions count dyonic degeneracies in the Hilbert space of four-dimensional toroidally compactified heterotic string theory, graded by electric and magnetic charges. The regularization is achieved by viewing the weighted sums of degeneracies as sums over charge excitations in the near-horizon attractor geometry of an arbitrarily chosen black hole background, and eliminating the unstable modes. This enables us to rewrite these sums in terms of indefinite theta functions. Background independence is then implemented by using the transformation property of indefinite theta functions under elliptic transformations, while modular transformations are used to make contact with semi-classical results in supergravity.
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