Hyperkahler metric and GMN ansatz on focus-focus fibrations
arXiv:1401.0352 · doi:10.1016/j.geomphys.2014.08.007
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.
20 pages. Comments are welcome
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