Direct Computation of Monodromy Matrices and Classification of 4d N=2 Heterotic--IIA Dual Vacua

TL;DR

This paper numerically computes monodromy matrices for 4d N=2 Heterotic--IIA dual vacua, revealing constraints on classification invariants and discussing related mathematical open problems.

Contribution

It introduces a numerical method to compute monodromy matrices without relying on geometric assumptions, aiding classification of string vacua.

Findings

Monodromy matrices are computed numerically for specific vacua.

Integrality constraints on monodromy matrices inform classification invariants.

Discussion of open mathematical problems related to period polynomials.

Abstract

We compute the monodromy matrices on the special geometry of 4d N=2 Heterotic--IIA dual vacua in some simple cases by numerical evaluation of the period integrals, without assuming geometric background. The integrality of the monodromy matrices constrains some classification invariants of the string vacua. We also mention some mathematical open problems on period polynomials for modular form with poles.