Givental graphs and inversion symmetry
Mathematical Physics
2013-04-19 v2 math.MP
Abstract
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 a Frobenius manifold. In this paper, we review the Givental group action on Frobenius manifolds in terms of Feynman graphs and 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.
Keywords
Cite
@article{arxiv.1201.4930,
title = {Givental graphs and inversion symmetry},
author = {P. Dunin-Barkowski and S. Shadrin and L. Spitz},
journal= {arXiv preprint arXiv:1201.4930},
year = {2013}
}
Comments
26 pages; revised according to the referees' remarks