English

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