On the integrable hierarchy for the resolved conifold
Algebraic Geometry
2022-04-12 v3 High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
We provide a direct proof of a conjecture of Brini relating the Gromov-Witten theory of the resolved conifold to the Ablowitz-Ladik integrable hierarchy at the level of primaries. In doing so, we use a functional representation of the Ablowitz-Ladik hierarchy as well as a difference equation for the Gromov-Witten 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.
Keywords
Cite
@article{arxiv.2101.11672,
title = {On the integrable hierarchy for the resolved conifold},
author = {Murad Alim and Arpan Saha},
journal= {arXiv preprint arXiv:2101.11672},
year = {2022}
}
Comments
18 pages, no figures. v3: modified statement of Proposition 2; Remarks 6 and 11 added; Remark 9 expanded; and other minor corrections