A Note on Symmetries of WDVV Equations

Details A Note on Symmetries of WDVV Equations A Note on Symmetries of WDVV Equations

2008-08-20

arxiv.org/abs/0808.2707v1

Theor. Math. Phys. 161 (2009) 1634-1646.

Nonlinear Sciences

Exactly Solvable and Integrable Systems

17 pages, latex, no figures

Scientific paper

We investigate symmetries of Witten-Dijkgraaf-E.Verlinde-H.Verlinde (WDVV) equations proposed by Dubrovin from bi-hamiltonian point of view. These symmetries can be viewed as canonical Miura transformations between genus-zero bi-hamiltonian systems of hydrodynamic type. In particular,we show that the moduli space of two-primary models under symmetries of WDVV can be characterized by the polytropic exponent $h$. Furthermore, we also discuss the transformation properties of free energy at genus-one level.

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