A novel method for computing torus amplitudes for $\mathbb{Z}_{N}$ orbifolds without the unfolding technique

TL;DR

This paper introduces a new, universal method for calculating torus amplitudes in Abelian belian 1Z_{N} orbifolds, avoiding the complex unfolding technique by using contour integrals over specific curves.

Contribution

It presents a novel approach that simplifies the computation of torus amplitudes in belian 1Z_{N} orbifolds, applicable to all such cases without unfolding.

Findings

Method applies universally to all Abelian belian 1Z_{N} orbifolds.

Utilizes contour integrals over curves in fundamental domains.

Avoids the traditional unfolding technique.

Abstract

A novel method for computing torus amplitudes in orbifold compactifications is suggested. It applies universally for every Abelian $\mathbb{Z}_{N}$ orbifold without requiring the unfolding technique. This method follows from the possibility of obtaining integrals over fundamental domains of every Hecke congruence subgroup $\Gamma_{0}[N]$ by computing contour integrals over one-dimensional curves uniformly distributed in these domains.