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 the sum of contributions associated with dual graphs of certain stable algebraic curves of genus two plus the socalled "genus two Gfunction." Conjecturally, the genus two Gfunction vanishes for a series of important examples of Frobenius manifolds associated with simple singularities, as well as for ℙ^{1}orbifolds with positive Euler characteristics. We explain the reasons for the conjecture and prove it in particular cases.
 Publication:

Russian Journal of Mathematical Physics
 Pub Date:
 July 2012
 DOI:
 10.1134/S1061920812030028
 arXiv:
 arXiv:1205.5990
 Bibcode:
 2012RJMP...19..273D
 Keywords:

 Mathematical Physics;
 Mathematics  Algebraic Geometry
 EPrint:
 37 pages, 3 figures, V2: the published version