TOPOLOGICAL LANDAU-GINZBURG FORMULATION AND INTEGRABLE STRUCTURE OF 2-DIMENSIONAL STRING THEORY

We construct a topological Landau-Ginsburg formulation of the two-dime nsional string at the self-dual radius. The model is an analytic conti nuation of the A(k+1) minimal model to k = -3. We compute the superpot ential and calculate tachyon correlators in the Landau-Ginzburg framew ork. The results are in complete agreement with matrix model calculati ons. We identify the momentum one tachyon as the puncture operator, no n-negative momentum tachyons as primary fields, and negative momentum ones as descendants. The model thus has an infinite number of primary fields, and the topological metric vanishes on the small phase space w hen restricted to these. We find a parity invariant multi-contact alge bra with irreducible contact terms of arbitrarily large number of fiel ds. The formulation of this Landau-Ginzburg description in terms of pe riod integrals coincides with the genus zero W1+infinity. identities o f two-dimensional string theory. We study the underlying Toda lattice integrable hierarchy in the Lax formulation and find that the Landau-G inzburg superpotential coincides with a derivative of the Baker-Akhiez er wave function in the dispersionless limit. This establishes a conne ction between the topological and integrable structures. Guided by thi s connection we derive relations formally analogous to the string equa tion.