https://scholars.lib.ntu.edu.tw/handle/123456789/631838
Title: | Quantum Riemann-Hilbert problems for the resolved conifold | Authors: | WU-YEN CHUANG | Keywords: | Donaldson-Thomas invariants | Multiple sine functions | Riemann-Hilbert problems; Mathematics - Algebraic Geometry; Mathematics - Algebraic Geometry; High Energy Physics - Theory; Primary: 14N35, Secondary: 35Q15 | Issue Date: | 1-Mar-2022 | Journal Volume: | 190 | Source: | Journal of Geometry and Physics | Abstract: | We study the quantum Riemann-Hilbert problems determined by the refined Donaldson-Thomas theory on the resolved conifold. Using the solutions to classical Riemann-Hilbert problems by Beidgeland, we give explicit solutions in terms of multiple sine functions with unequal parameters. The new feature of the solutions is that the valid region of the quantum parameter $q^{\frac{1}{2}}=\exp(\pi i \tau)$ varies on the space of stability conditions and BPS $t$-plane. Comparing the solutions with the partition function of refined Chern-Simons theory and invoking large $N$ string duality, we find that the solution contains the non-perturbative completion of the refined topological string on the resolved conifold. Therefore solving the quantum Riemann-Hilbert problems provides a possible non-perturbative definition for the Donaldson-Thomas theory. |
Description: | 21 pages, to appear in Journal of Geometry and Physics |
URI: | https://scholars.lib.ntu.edu.tw/handle/123456789/631838 | ISSN: | 03930440 | DOI: | 10.1016/j.geomphys.2023.104860 |
Appears in Collections: | 數學系 |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.