Regularized Integrals on Elliptic Curves and Holomorphic Anomaly Equations
Differential Geometry
2023-06-28 v2 High Energy Physics - Theory
Mathematical Physics
Complex Variables
math.MP
Number Theory
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 -cycle integrals and establish their relations with those for the regularized integrals.
Keywords
Cite
@article{arxiv.2205.14562,
title = {Regularized Integrals on Elliptic Curves and Holomorphic Anomaly Equations},
author = {Si Li and Jie Zhou},
journal= {arXiv preprint arXiv:2205.14562},
year = {2023}
}
Comments
Appendices added. To appear in Communications in Mathematical Physics