Rankin-Selberg methods for closed strings on orbifolds
Rankin-Selberg methods for closed strings on orbifolds
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Orbifolds 上闭弦的 Rankin-Selberg 方法
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
B. Pioline
中科院分区：
文献类型：
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作者：
C. Angelantonj;I. Florakis;B. Pioline
在最近的工作中，我们已经开发了一个新的展开方法计算单圈模积分的弦理论涉及的Narain配分函数，并可能，弱几乎全纯椭圆亏格。与传统的方法不同，Narain格在展开过程中不起任何作用，T-对偶在所有步骤中都保持明显，不需要选择Weyl室，振幅的解析结构是透明的。本文将这一过程推广到Abel $ {{mathbb{Z}}_N} $ orbifolds的情形，其中被积函数分解为orbifolds块的和，这些块可以组织成Hecke同余子群Γ0（N）的轨道。因此，原来的模积分减少到一个积分的基本域的Γ0（N），我们然后评估我们以前的技术。例如，我们的方法适用于评价闭弦模型低能有效作用下的BPS饱和耦合的单圈修正、凯勒度规的量子修正以及超弦真空的自由能。
A bstractIn recent work we have developed a new unfolding method for computing one-loop modular integrals in string theory involving the Narain partition function and, possibly, a weak almost holomorphic elliptic genus. Unlike the traditional approach, the Narain lattice does not play any role in the unfolding procedure, T-duality is kept manifest at all steps, a choice of Weyl chamber is not required and the analytic structure of the amplitude is transparent. In the present paper, we generalise this procedure to the case of Abelian $ {{mathbb{Z}}_N} $ orbifolds, where the integrand decomposes into a sum of orbifold blocks that can be organised into orbits of the Hecke congruence subgroup Γ0(N). As a result, the original modular integral reduces to an integral over the fundamental domain of Γ0(N), which we then evaluate by extending our previous techniques. Our method is applicable, for instance, to the evaluation of one-loop corrections to BPS-saturated couplings in the low energy effective action of closed string models, of quantum corrections to the Kähler metric and, in principle, of the free-energy of superstring vacua.