Hyperkahler metric and GMN ansatz on focus-focus fibrations
Differential Geometry
2014-08-26 v1 Mathematical Physics
math.MP
Symplectic Geometry
Abstract
In this paper, we study hyperkahler metric and practice GMN's construction of hyperkahler metric on focus-focus fibrations. We explicitly compute the action-angel coordinates on the local model of focus-focus fibration, and show its semi-global invariant should be harmonic to admit a compatible holomorphic 2-form. Then we study the canonical semi-flat metric on it. After the instanton correction, finally we get a re-construction of the generalized Ooguri-Vafa metric.
Keywords
Cite
@article{arxiv.1401.0352,
title = {Hyperkahler metric and GMN ansatz on focus-focus fibrations},
author = {Jie Zhao},
journal= {arXiv preprint arXiv:1401.0352},
year = {2014}
}
Comments
20 pages. Comments are welcome