Resurgence and Riemann--Hilbert problems for orientifolded conifolds
Wu-yen Chuang, Yi-Jing Tseng
TL;DR
This work extends resurgence analysis to orientifolded conifolds, showing that the perturbative free energy for $SO/Sp$ Chern–Simons theory on $S^3$ admits a complete nonperturbative completion expressible through double and triple sine functions. By computing the Borel transform of the genus expansion and its Stokes jumps, the authors extract unoriented Donaldson–Thomas invariants and encode them in a Riemann–Hilbert framework, proposing a candidate tau-function linked to $H^{\dagger}$. The full nonperturbative free energy is presented in closed form via $\log G_3$ and $\log F_2$ terms, with explicit jump formulas that match the expected DT data. The RH problem for orientifolded conifolds is formulated, although a full identification of the tau-function with the crosscap energy remains an open direction. Overall, the paper uncovers a coherent resurgent and RH structure for orientifolded backgrounds, suggesting broader applicability to other gauge groups and refined theories.
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 $τ$-functions.