Hadamard products and BPS networks

Mohamed Elmi

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arXiv · 2311.08683

Hadamard products and BPS networks

Mohamed Elmi

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Abstract

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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Mohamed Elmi. 2023-11-15. Hadamard products and BPS networks. https://arxiv.org/abs/2311.08683

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