Direct computation of monodromy matrices and classification of 4d $$ \mathcal{N} $$ = 2 heterotic-IIA dual vacua

Abstract

Abstract We compute the monodromy matrices on the special geometry of 4d $$ \mathcal{N} $$ N = 2 Heterotic-IIA dual vacua in some simple cases by numerical evaluation of the period integrals, without assuming a 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 forms with poles.