Hadamard products and BPS networks
High Energy Physics - Theory
2023-12-25 v2 Algebraic Geometry
Symplectic Geometry
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.
Cite
@article{arxiv.2311.08683,
title = {Hadamard products and BPS networks},
author = {Mohamed Elmi},
journal= {arXiv preprint arXiv:2311.08683},
year = {2023}
}
Comments
37 pages, 9 figures, some typos corrected