On the integrable hierarchy for the resolved conifold

Murad Alim; Arpan Saha

doi:10.48550/arXiv.2101.11672

On the integrable hierarchy for the resolved conifold

Murad Alim, Arpan Saha

Research output: Working paper › Preprint

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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.

Original language	Undefined/Unknown
Publisher	arXiv
DOIs	https://doi.org/10.48550/arXiv.2101.11672
Publication status	Published - 27 Jan 2021

Keywords

math.AG
hep-th
math-ph
math.MP
14N35, 53D45

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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. ",

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