Title | Virasoro Symmetries of the Extended Toda Hierarchy |
Publication Type | Journal Article |
Year of Publication | 2004 |
Authors | Dubrovin, B, Youjin, Z |
Journal | Comm. Math.\\nPhys. 250 (2004) 161-193. |
Abstract | We prove that the extended Toda hierarchy of \\\\cite{CDZ} admits nonabelian Lie algebra of infinitesimal symmetries isomorphic to the half of the Virasoro algebra. The generators $L_m$, $m\\\\geq -1$ of the Lie algebra act by linear differential operators onto the tau function of the hierarchy. We also prove that the tau function of a generic solution to the extended Toda hierarchy is annihilated by a combination of the Virasoro operators and the flows of the hierarchy. As an application we show that the validity of the Virasoro constraints for the $CP^1$ Gromov-Witten invariants and their descendents implies that their generating function is the logarithm of a particular tau function of the extended Toda hierarchy. |
URL | http://hdl.handle.net/1963/2544 |
DOI | 10.1007/s00220-004-1084-9 |
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