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arXiv · 2205.14562

Regularized Integrals on Elliptic Curves and Holomorphic Anomaly Equations

Si Li·Jie Zhou
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Abstract

We derive residue formulas for the regularized integrals (introduced by Li-Zhou) on configuration spaces of elliptic curves. Based on these formulas, we prove that the regularized integrals satisfy holomorphic anomaly equations, providing a mathematical formulation of the so-called contact term singularities. We also discuss residue formulas for the ordered $A$-cycle integrals and establish their relations with those for the regularized integrals.

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BibTeXRIS

Si Li, Jie Zhou. 2022-05-29. Regularized Integrals on Elliptic Curves and Holomorphic Anomaly Equations. https://doi.org/10.1007/s00220-023-04647-3

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