Resurgence and holonomy of the $\phi^{2k}$ model in zero dimension

TL;DR

This paper investigates the resurgence properties of zero-dimensional field theory partition functions, demonstrating they satisfy linear differential equations with polynomial coefficients, and uses holonomic functions to improve growth estimates of formal series.

Contribution

It introduces a novel approach using holonomic functions to establish resurgence properties of zero-dimensional field theory partition functions, extending previous combinatorial results.

Findings

Partition functions satisfy linear differential equations with polynomial coefficients.

Resurgence properties are proven using stability results and holonomic functions.

Growth estimates of formal series are improved over previous combinatorial methods.

Abstract

We describe the resurgence properties of some partition functions corresponding to field theories in dimension 0. We show that these functions satisfy linear differential equations with polynomial coefficients and then use elementary stability results or holonomic functions to prove resurgence properties, enhancing previously known results on growth estimates for the formal series involved, which had been obtained through a delicate combinatorics.