Direct computation of period polynomials and classification of K3-fibred Calabi--Yau threefolds

2022/12/15 by Yuichi Enoki, Enoki, Yuichi, Yotaro Sato +3
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th)

paper · pdf · doi:10.48550/arxiv.2212.07948

openalex publication_date 2022/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

One can assign to four-dimensional N=2 supersymmetric Heterotic string vacua a set of classification invariants including a lattice Λ_S and vector-valued modular forms. Some of the classification invariants are constrained by the condition that the Coulomb branch monodromy matrices should be integer-valued. We computed numerically the period polynomials of meromorphic cusp forms for some rank-1 Λ_S; we then computed the monodromy matrices and extracted general patterns of the constraints on the invariants. The constraints we got imply that a large fraction of the Heterotic string vacua we studied satisfy the necessary conditions for a non-linear sigma model interpretation in the dual Type IIA description. Our computation can also be used to identify diffeomorphism classes of real six-dimensional manifolds that cannot be realized by K3-fibred Calabi--Yau threefolds.

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