On the Genus Two Free Energies for Semisimple Frobenius Manifolds

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 ${\mathbf{P}}^1$-orbifolds with positive Euler characteristics. We explain the reasons for such Conjecture and prove it in certain particular cases.

37 pages, 3 figures, V2: the published version

References in corpus (1)

• Tau Functions and Virasoro Symmetries for Drinfeld-Sokolov Hierarchies

Cited by in corpus (3)

• Extended affine Weyl groups of BCD type, Frobenius manifolds and their Landau-Ginzburg superpotentials
• Proof of a Conjecture on the Genus Two Free Energy Associated to the A_n Singularity
• On Equivariant Gromov--Witten Invariants of Resolved Conifold with Diagonal and Anti-Diagonal Actions