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- W2134374754 abstract "We study two instanton correction problems ofHitchin's moduli spaces along with their wall crossing formulas.The hyperkahler metric of a Hitchin's moduli space can be put intoan instanton-corrected form according to physicists Gaiotto, Mooreand Neitzke. The problem boils down to the construction of a set ofspecial coordinates which can be constructed as Fock-Goncharovcoordinates associated with foliations of quadratic differentialson a Riemann surface. A wall crossing formula of Kontsevich andSoibelman arises both as a crucial consistency condition and aneffective computational tool. On the other hand Gross and Sieberthave succeeded in determining instanton corrections of complexstructures of Calabi-Yau varieties in the context of mirrorsymmetry from a singular affine structure with additional data. Wewill show that the two instanton correction problems are equivalentin an appropriate sense via the identification of the wall crossingformulas in the metric problem with consistency conditions in thecomplex structure problem. This is a nontrivial statement of mirrorsymmetry of Hitchin's moduli spaces which till now has been mostlystudied in the framework of geometric Langlands duality. Thisresult provides examples of Calabi-Yau varieties where theinstanton correction (in the sense of mirror symmetry) of metricsand complex structures can be determined. This equivalence alsorelates certain enumerative problems in foliations to some gluingconstructions of affine varieties." @default.
- W2134374754 created "2016-06-24" @default.
- W2134374754 creator A5016666687 @default.
- W2134374754 date "2011-01-01" @default.
- W2134374754 modified "2023-09-27" @default.
- W2134374754 title "Instanton Correction, Wall Crossing And Mirror Symmetry Of Hitchin's Moduli Spaces" @default.
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