The Two-Dimensional String as a Topological Field Theory

TL;DR

This paper demonstrates the equivalence of a specific topological field theory to the compactified c=1 string, providing calculable partition functions and correlators, and relating it to the KPZ formulation of non-critical string theory.

Contribution

It introduces a topological field theory formulation of the c=1 string, enabling explicit calculations of key string theory quantities and connecting to the KPZ framework.

Findings

Equivalence between topological field theory and c=1 string.

Calculable genus-g partition functions and multi-tachyon correlators.

Relation to the KPZ formulation of non-critical string theory.

Abstract

A certain topological field theory is shown to be equivalent to the compactified c=1 string. This theory is described in both Kazama-Suzuki coset and Landau-Ginzburg formulations. The genus-g partition function and genus-0 multi-tachyon correlators of the c=1 string are shown to be calculable in this approach. The KPZ formulation of non-critical string theory has a natural relation to this topological model. (Talk given at the Nato Advanced Research Workshop on `New Developments in String Theory, Conformal Models and Topological Field Theory', Cargese, May 12-21 1993.)