Work

The Regularity of ODEs and Thimble Integrals with Respect to Borel Summation

Year: 2025

Type: article

Abstract: Through Borel summation, one can often reconstruct an analytic solution of a problem from its asymptotic expansion. We view the effectiveness of Borel summation as a regularity property of the solution, and we show that the solutions of certain differential equation and integration problems are regular in this sense. By taking a geometric perspective on the Laplace and Borel transforms, we also clarify why ''Borel regular'' solutions are associated with special points on the Borel plane. The particular classes of problems we look at are level $1$ ODEs and exponential period integrals over one-dimensional Lefschetz thimbles. To expand the variety of examples available in the literature, we treat various examples of these problems in detail.

Source: Symmetry Integrability and Geometry Methods and Applications

DOI: 10.3842/sigma.2025.101

Authors: Laboratoire Mathématique d'Orsay, France, Veronica Fantini, Aaron Fenyes, Studio Infinity, USA

Institutions: Laboratoire de Mathématiques d'Orsay, Infinity (United States)

Language: English

Topic: Mathematical and Theoretical Analysis

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: European Commission, H2020 European Research Council

Awards: G434337789, Recursive and Exact New Quantum Theory