A Hyperk\'ahler geometry associated to the BPS structure of the resolved conifold

Autor:	Alim, Murad, Saha, Arpan, Tulli, Iván
Rok vydání:	2021
Předmět:	Mathematics - Differential Geometry High Energy Physics - Theory Mathematical Physics Mathematics - Algebraic Geometry
Druh dokumentu:	Working Paper
DOI:	10.1016/j.geomphys.2022.104618
Popis:	We associate to the resolved conifold an affine special K\"{a}hler (ASK) manifold of complex dimension 1, and an instanton corrected hyperk\"{a}hler (HK) manifold of complex dimension 2. We describe these geometries explicitly, and show that the instanton corrected HK geometry realizes an Ooguri-Vafa-like smoothing of the semi-flat HK metric associated to the ASK geometry. On the other hand, the instanton corrected HK geometry associated to the resolved conifold can be described in terms of a twistor family of two holomorphic Darboux coordinates. We study a certain conformal limit of the twistor coordinates, and conjecture a relation to a solution of a Riemann-Hilbert problem previously considered by T. Bridgeland. Comment: 49 pages, references added and typos fixed. Previous theorem 43 and corollary 44 revised, and the rest of the results unchanged
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2106.11976 Zobrazit plný text záznamu View this record from Arxiv