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Teoreticheskaya i Matematicheskaya Fizika, 2009, Volume 161, Number 3, Pages 367–381
DOI: https://doi.org/10.4213/tmf6447 (Mi tmf6447) 		 
The WDVV symmetries in two-primary models

Yu-Tung Chena, Niann-Chern Leeb, Ming-Hsien Tuca

a 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
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DOI: https://doi.org/10.4213/tmf6447
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
English version:
Theoretical and Mathematical Physics, 2009, Volume 161, Issue 3, Pages 1634–1646
DOI: https://doi.org/10.1007/s11232-009-0151-y
Bibliographic databases:
Language: Russian
Citation: Yu-Tung Chen, Niann-Chern Lee, Ming-Hsien Tu, “The WDVV symmetries in two-primary models”, TMF, 161:3 (2009), 367–381; Theoret. and Math. Phys., 161:3 (2009), 1634–1646
Citation in format AMSBIB
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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