On the integrable hierarchy for the resolved conifold. Issue 5 (4th June 2022)

• Record Type: Journal Article
• Authors: Alim, Murad; Saha, Arpan
• Is Part Of: Bulletin of the London Mathematical Society. Volume 54:Issue 5(2022)
• Page Start: 2014
• Page End: 2031
• Publication Date: 2022-06-04
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1112/blms.12676
• Languages: English
• ISSNs: 0024-6093

Abstract

Abstract: We provide a direct proof of a conjecture of Brini relating the Gromov–Witten (GW) theory of the resolved conifold to the Ablowitz–Ladik (AL) integrable hierarchy at the level of primaries. In doing so, we use a functional representation of the AL hierarchy as well as a difference equation for the GW potential. In particular, we express certain distinguished solutions of the difference equation in terms of an analytic function which is a specialization of a Tau function put forward by Bridgeland in the study of wall‐crossing phenomena of Donaldson–Thomas invariants.