String Duality and Modular Forms

TL;DR

This paper investigates string dualities by comparing modular forms related to threshold corrections in heterotic and type IIA string theories on specific Calabi-Yau manifolds, testing the duality conjecture.

Contribution

It provides explicit comparisons of modular forms and threshold corrections for three Calabi-Yau cases, advancing understanding of heterotic/type IIA duality.

Findings

Identification of modular forms matching between heterotic and type IIA sides.

Verification of duality in specific Calabi-Yau compactifications.

Enhanced understanding of string threshold corrections in dual models.

Abstract

Tests of duality between heterotic strings on $K3\times T^2$ (restricted on certain Narain moduli subspaces) and type IIA strings on K3-fibered Calabi-Yau threefolds are attempted in the weak coupling regime on the heterotic side by identifying pertinent modular forms related to the computations of string threshold corrections. Concretely we discuss in parallel the three cases associated with Calabi-Yau manifolds $(A):X(6,2,2,1,1)_{2}^{-252}$, $(B):X(12,8,2,1,1)_{3}^{-480}$ and $(C):X(10,3,3,2,2)_{4}^{-132}$ on the type IIA side.