D-brane Masses at Special Fibres of Hypergeometric Families of Calabi–Yau Threefolds, Modular Forms, and Periods

Bönisch, Kilian; Klemm, Albrecht; Scheidegger, Emanuel; Zagier, Don

doi:10.1007/s00220-024-05006-6

Commun. Math. Phys.

2024

DOI: 10.1007/s00220-024-05006-6

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D-brane Masses at Special Fibres of Hypergeometric Families of Calabi–Yau Threefolds, Modular Forms, and Periods

Kilian Bönisch,

Albrecht Klemm,

Emanuel Scheidegger

et al.

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2024

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Cited by 2 publications

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Hadamard products and BPS networks

Elmi

2024

J. High Energ. Phys.

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We study examples of fourth-order Picard-Fuchs operators that are Hadamard products of two second-order Picard-Fuchs operators. Each second-order Picard-Fuchs operator is associated with a family of elliptic curves, and the Hadamard product computes period integrals on the fibred product of the two elliptic surfaces. We construct 3-cycles on this geometry as the union of 2-cycles in the fibre over contours on the base. We then use the special Lagrangian condition to constrain the contours on the base. This leads to a construction that is reminiscent of spectral networks and exponential networks that have previously appeared in string theory literature.

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Hadamard products and BPS networks

Elmi

2024

J. High Energ. Phys.

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Beyond large complex structure: quantized periods and boundary data for one-modulus singularities

Bastian,

van de Heisteeg,

Schlechter

2024

J. High Energ. Phys.

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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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D-brane Masses at Special Fibres of Hypergeometric Families of Calabi–Yau Threefolds, Modular Forms, and Periods

Cited by 2 publications

References 80 publications

Hadamard products and BPS networks

Hadamard products and BPS networks

Beyond large complex structure: quantized periods and boundary data for one-modulus singularities

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