Exact Monodromy Group of N=2 Heterotic Superstring

TL;DR

The paper investigates nonperturbative structure in an $N=2$ heterotic string by exploiting a string–string duality with Type II on a Calabi–Yau with $b_{1,1}=2$ and $b_{1,2}=86$. By analyzing the Type II monodromy group, it identifies the exact symmetry group containing the perturbative heterotic duality and the nonperturbative monodromies of the rigid $SU(2)$ theory, including a stringy monodromy that exchanges $S$ and $T$ and a strong-coupling line with massless dyons. The perturbative prepotentials match across the dual theories, and the heterotic monodromies embed into the Type II symplectic monodromy group $\mathcal G\subset Sp(6,\mathbb{Z})$, providing a nontrivial test of string–string duality. The analysis also shows that the perturbative $SU(2)$ enhancement splits into nonperturbative branches and that new dilaton‑related monodromies arise, illustrating a richer nonperturbative landscape linked to conifold and strong‑coupling phenomena on the Type II side.

Abstract

We describe an $N=2$ heterotic superstring model of rank-3 which is dual to the type-II string compactified on a Calabi-Yau manifold with Betti numbers $b_{1,1}=2$ and $b_{1,2}=86$. We show that the exact duality symmetry found from the type II realization contains the perturbative duality group of the heterotic model, as well as the exact quantum monodromies of the rigid $SU(2)$ super-Yang-Mills theory. Moreover, it contains a non-perturbative monodromy which is stringy in origin and corresponds roughly to an exchange of the string coupling with the compactification radius.