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

The Toda lattice hierarchy is discussed in connection with the topological description of the c = 1 string theory compactified at the selfdual 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 W1+∞ 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.