The WDVV symmetries in two-primary models

Yu-Tung Chen^a, Niann-Chern Lee^b, Ming-Hsien Tu<sup>ca

a</sup> Department of Computer Science, National Defense University, Tauyuan, Taiwan
^b General Education Center, National Chin-Yi University of Technology, Taichung, Taiwan
^c Department of Physics, National Chung Cheng University, Chiayi, Taiwan

Abstract: From the bi-Hamiltonian standpoint, we investigate symmetries of Witten–Dijkgraaf–Verlinde–Verlinde (WDVV) equations proposed by Dubrovin. 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 the WDVV equations can be parameterized by the polytropic exponent $h$. We discuss the transformation properties of the free energy at the genus-one level.

Keywords: Frobenius manifold, WDVV equation, bi-Hamiltonian structure, primary free energy, dToda hierarchy, Benney hierarchy, dDym hierarchy, polytropic gas dynamics.

Received: 09.03.2009

DOI: 10.4213/tmf6447

 English version: Theoretical and Mathematical Physics, 2009, 161:3, 1634–1646

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