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arXiv · 2212.07948

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

Yuichi Enoki·Yotaro Sato·Taizan Watari
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Abstract

One can assign to four-dimensional N=2 supersymmetric Heterotic string vacua a set of classification invariants including a lattice $\Lambda_S$ 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 $\Lambda_S$; 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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Yuichi Enoki, Yotaro Sato, Taizan Watari. 2022-12-15. Direct computation of period polynomials and classification of K3-fibred Calabi--Yau threefolds. https://arxiv.org/abs/2212.07948

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