Resurgence and Riemann--Hilbert problems for orientifolded conifolds

TL;DR

This paper performs a resurgence analysis of orientifolded conifold partition functions, deriving nonperturbative results, unoriented Donaldson--Thomas invariants, and exploring related Riemann--Hilbert problems and tau-functions.

Contribution

It introduces a comprehensive resurgence framework for orientifolded conifolds, connecting nonperturbative partition functions with Donaldson--Thomas invariants and Riemann--Hilbert problems.

Findings

Derived full nonperturbative partition functions using multiple sine functions.

Obtained unoriented Donaldson--Thomas invariants from Stokes jump analysis.

Explored Riemann--Hilbert problems and tau-functions associated with the invariants.

Abstract

We perform a resurgence analysis of the perturbative partition functions of orientifolded conifolds and obtain the full nonperturbative partition functions in terms of multiple sine functions. We derive the unoriented Donaldson--Thomas invariants from the analysis of associated Stokes jumps. We further discuss the Riemann--Hilbert problems defined by the Donaldson--Thomas invariants arising from orientifolded conifolds and the corresponding $\tau$-functions.