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On the Genus Two Free Energies for Semisimple Frobenius Manifolds

Authors
  • Dubrovin, Boris
  • Liu, Si-Qi
  • Zhang, Youjin
Type
Published Article
Publication Date
May 05, 2013
Submission Date
May 27, 2012
Identifiers
DOI: 10.1134/S1061920812030028
Source
arXiv
License
Yellow
External links

Abstract

We represent the genus two free energy of an arbitrary semisimple Frobenius manifold as a sum of contributions associated with dual graphs of certain stable algebraic curves of genus two plus the so-called "genus two G-function". Conjecturally the genus two G-function vanishes for a series of important examples of Frobenius manifolds associated with simple singularities as well as for ${\bf P}^1$-orbifolds with positive Euler characteristics. We explain the reasons for such Conjecture and prove it in certain particular cases.

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