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 P1-orbifolds with positive Euler characteristics. We explain the reasons for such Conjecture and prove it in certain particular cases.
On the genus two free energies for semisimple Frobenius manifolds
Dubrovin, Boris;
2012-01-01
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 P1-orbifolds with positive Euler characteristics. We explain the reasons for such Conjecture and prove it in certain particular cases.File in questo prodotto:
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