Tuesday, May 29, 2012

1205.5990 (Boris Dubrovin et al.)

On the Genus Two Free Energies for Semisimple Frobenius Manifolds    [PDF]

Boris Dubrovin, Si-Qi Liu, Youjin Zhang
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.
View original: http://arxiv.org/abs/1205.5990

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