轨道上闭弦的Rankin-Selberg方法
Rankin-Selberg methods for closed strings on orbifolds
摘要：
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论涉及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 Z_N轨道折叠的情形，其中被积函数分解为轨道折叠块之和，这些块可组织为Hecke同余子群Γ_0（N）的轨道。结果，原来的模积分简化为在Γ_0（N）的基本区域上的积分，然后我们通过扩展我们以前的方法来计算。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。
英文摘要：
In 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 Z_N orbifolds, where the integrand decomposes into a sum of orbifold blocks that can be organised into orbits of the Hecke congruence subgroup Γ_0(N). As a result, the original modular integral reduces to an integral over the fundamental domain of Γ_0(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.
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