Rankin-Selberg methods for closed strings on orbifolds

TL;DR

This paper extends a novel unfolding method for one-loop string integrals to Abelian Z_N orbifolds, simplifying calculations while keeping T-duality manifest, and applies it to various string theory corrections.

Contribution

It generalizes a new unfolding technique to orbifolds, enabling more transparent and efficient evaluation of modular integrals in string theory.

Findings

Method applicable to one-loop corrections in string models

Simplifies evaluation of orbifold modular integrals

Maintains T-duality throughout the process

Abstract

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 {\Gamma}_0(N). As a result, the original modular integral reduces to an integral over the fundamental domain of {\Gamma}_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 K\"ahler metric and, in principle, of the free-energy of superstring vacua.