Givental graphs and inversion symmetry

Details Givental graphs and inversion symmetry Givental graphs and inversion symmetry

2012-01-24

arxiv.org/abs/1201.4930v1

Physics

Mathematical Physics

23 pages

Scientific paper

Inversion symmetry is a very non-trivial discrete symmetry of Frobenius manifolds. It was obtained by Dubrovin from one of the elementary Schlesinger transformations of a special ODE associated to Frobenius manifold. In this paper, we review the Givental group action on Frobenius manifolds in terms of Feynman graphs and then we obtain an interpretation of the inversion symmetry in terms of the action of the Givental group. We also consider the implication of this interpretation of the inversion symmetry for the Schlesinger transformations and for the Hamiltonians of the associated principle hierarchy.

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