Conifold singularities, resumming instantons and non-perturbative mirror symmetry

TL;DR

The work analyzes non-perturbative corrections to the type IIB hypermultiplet moduli space near a Calabi–Yau conifold point where a two-cycle shrinks, showing that D1-instantons resolve the conifold singularity and that a resummation of instantons exactly reproduces the Ooguri–Vafa result for membrane instantons on the type IIA side. By combining the rigid c-map, projective superspace techniques, and Poisson resummation, the authors demonstrate that the IIB/HM metric matches the IIA/VMC metric in the conifold limit, thereby proving non-perturbative mirror symmetry in the string coupling. The results provide a concrete non-perturbative check of CY conifold physics and clarify how instanton sectors map across the IIA/IIB pair under mirror symmetry. Overall, the paper solidifies the view that mirror symmetry persists at the full quantum level, including instanton corrections, in the conifold regime.

Abstract

We determine the instanton corrected hypermultiplet moduli space in type IIB compactifications near a Calabi-Yau conifold point where the size of a two-cycle shrinks to zero. We show that D1-instantons resolve the conifold singularity caused by worldsheet instantons. Furthermore, by resumming the instanton series, we reproduce exactly the results obtained by Ooguri and Vafa on the type IIA side, where membrane instantons correct the hypermultiplet moduli space. Our calculations therefore establish that mirror symmetry holds non-perturbatively in the string coupling.

Figures (1)

• Figure 1: Illustration of the CY$_3$ moduli space close to a conifold point. For more information on conifold singularities we refer to SBHGreene:1996dh.