A Hyperk\"ahler geometry associated to the BPS structure of the resolved conifold
Abstract
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.
Keywords
Cite
@article{arxiv.2106.11976,
title = {A Hyperk\"ahler geometry associated to the BPS structure of the resolved conifold},
author = {Murad Alim and Arpan Saha and Iván Tulli},
journal= {arXiv preprint arXiv:2106.11976},
year = {2022}
}
Comments
49 pages, references added and typos fixed. Previous theorem 43 and corollary 44 revised, and the rest of the results unchanged