Mathematical Structures of Non-perturbative Topological String Theory: From GW to DT Invariants

Murad Alim, Arpan Saha, Joerg Teschner, Iván Tulli*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)
3 Downloads (Pure)

Abstract

We study the Borel summation of the Gromov–Witten potential for the resolved conifold. The Stokes phenomena associated to this Borel summation are shown to encode the Donaldson–Thomas (DT) invariants of the resolved conifold, having a direct relation to the Riemann–Hilbert problem formulated by Bridgeland (Invent Math 216(1), 69–124, 2019). There exist distinguished integration contours for which the Borel summation reproduces previous proposals for the non-perturbative topological string partition functions of the resolved conifold. These partition functions are shown to have another asymptotic expansion at strong topological string coupling. We demonstrate that the Stokes phenomena of the strong-coupling expansion encode the DT invariants of the resolved conifold in a second way. Mathematically, one finds a relation to Riemann–Hilbert problems associated to DT invariants which is different from the one found at weak coupling. The Stokes phenomena of the strong-coupling expansion turn out to be closely related to the wall-crossing phenomena in the spectrum of BPS states on the resolved conifold studied in the context of supergravity by Jafferis and Moore (Wall crossing in local Calabi Yau manifolds, arXiv:0810.4909, 2008).
Original languageEnglish
Pages (from-to)1039–1101
Number of pages63
JournalCommunications in Mathematical Physics
Volume399
Early online date27 Nov 2022
DOIs
Publication statusPublished - Apr 2023

Keywords

  • hep-th
  • math-ph
  • math.AG
  • math.DG
  • math.MP

Fingerprint

Dive into the research topics of 'Mathematical Structures of Non-perturbative Topological String Theory: From GW to DT Invariants'. Together they form a unique fingerprint.

Cite this