Toda Lattice Hierarchy and the Topological Description of the c=1 String Theory

Details Toda Lattice Hierarchy and the Topological Description of the c=1 String Theory Toda Lattice Hierarchy and the Topological Description of the c=1 String Theory

1994-04-11

arxiv.org/abs/hep-th/9404056v1

Phys.Lett. B331 (1994) 330-334

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, Latex file, UT-674

Scientific paper

10.1016/0370-2693(94)91060-X

The Toda lattice hierarchy is discussed in connection with the topological description of the $c=1$ string theory compactified at the self-dual radius. It is shown that when special constraints are imposed on the Toda hierarchy, it reproduces known results of the $c=1$ string theory, in particular the $W_{1+\infty}$ relations among tachyon correlation functions. These constraints are the analogues of string equations in the topological minimal theories. We also point out that at $c=1$ the Landau-Ginzburg superpotential becomes simply a $U(1)$ current operator.

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