2021/01/27 by Murad Alim, Alim, Murad, Arpan Saha +1
Mathematics · Physics and Astronomy · #14N35 #53D45 #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2101.11672
openalex publication_date 2021/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.