Givental graphs and inversion symmetry

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.

26 pages; revised according to the referees' remarks

References in corpus (2)

• On deformations of quasi-Miura transformations and the Dubrovin-Zhang bracket
• Witten's conjecture, Virasoro conjecture, and invariance of tautological equations

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• 4D limit of melting crystal model and its integrable structure
• Generalized cohomological field theories in the higher order formalism
• Conjugate Frobenius manifold and inversion symmetry