String-dual $F_1$-Function in the Three Parameter Model

TL;DR

This paper verifies string-string duality by computing the holomorphic $F_1$-function, which describes one-loop gravitational couplings in a specific dual pair of heterotic and type IIA string theories.

Contribution

It provides a detailed computation of the $F_1$-function in the three-parameter model, confirming the duality between heterotic and type IIA string theories.

Findings

Confirmation of string-string duality through $F_1$-function computation

Matching of gravitational couplings in dual theories

Validation of the proposed dual pair involving $K3\times T^2$ and a Calabi-Yau manifold

Abstract

Computation of the holomorphic $F_1$-function describing one-loop gravitational couplings of vectormultiplets is shown to confirm string-string duality of the proposed dual pair consisting of the heterotic string on $K3\times T^2$ with gauge group $U(1)^4$ and the type IIA string on the Calabi-Yau $WP^4_{1,1,2,8,12}(24)$.