Abstract
We study periods in an integral basis near all possible singularities in one-dimensional complex structure moduli spaces of Calabi-Yau threefolds. Near large complex structure points these asymptotic periods are well understood in terms of the topological data of the mirror Calabi-Yau manifold. The aim of this work is to characterize the period data near other boundaries in moduli space such as conifold and K-points. Using results from Hodge theory, we provide the general form of these periods in a quantized three-cycle basis. Based on these periods we compute the prepotential and related physical couplings of the underlying supergravity theory. Moreover, we elucidate the meaning of the model-dependent coefficients that appear in these expressions: these can be identified with certain topological and arithmetic numbers associated to the singular geometry at the moduli space boundary. We illustrate our findings by studying a wide set of examples.
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Acknowledgments
We would like to thank Thomas Grimm for early collaboration on this work. Moreover, it is a pleasure to thank Kilian Bönisch, Chuck Doran, Matt Kerr, Erik Plauschinn, John Stout, and Max Wiesner for discussions and correspondence. The research of LS is supported, in part, by the Dutch Research Council (NWO) via a Start-Up grant and a Vici grant.
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Bastian, B., van de Heisteeg, D. & Schlechter, L. Beyond large complex structure: quantized periods and boundary data for one-modulus singularities. J. High Energ. Phys. 2024, 151 (2024). https://doi.org/10.1007/JHEP07(2024)151
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DOI: https://doi.org/10.1007/JHEP07(2024)151