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On the genus two free energies for semisimple Frobenius manifolds |
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| Authors: | Boris Dubrovin Si-Qi Liu Youjin Zhang |
| Institution: | 1. SISSA, Via Bonomea 265, 34136, Trieste, Italy 3. Laboratory of Geometric Methods in Mathematical Physics, Moscow State University, Moscow, 119991, Russia 4. Steklov Mathematical Institute, Russian Academy of Sciences, 117333, Moscow, Russia 2. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, P. R. China |
| 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 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 ?1-orbifolds with positive Euler characteristics. We explain the reasons for the conjecture and prove it in particular cases. |
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