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

Abstract

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.

11 pages, Latex file, UT-674

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• Topological 2D String Theory: Higher-genus Amplitudes and W-infinity Identities
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• Topological Field Theory Interpretations and LG Representation of c=1 String Theory
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• Thermodynamic limit of random partitions and dispersionless Toda hierarchy
• Integrable structure of melting crystal model with external potentials
• c=1 discrete states correlators via W${}_{1+\infty }$ constraints
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• Vortex condensation and black hole in the matrix model of 2-d string theory
• Quiver matrix model of ADHM type and BPS state counting in diverse dimensions
• Remarks on tree-level topological string theories