CM < 1 string theory as a constrained topological sigma model

Abstract

It has been argued by Ishikawa and Kato that by making use of a specific bosonization, c M = 1 string theory can be regarded as a constrained topological sigma model. We generalize their construction for any ( p, q) minimal model coupled to two dimensional (2d) gravity and show that the energy-momentum tensor and the topological charge of a constrained topological sigma model can be mapped to the energy-momentum tensor and the BRST charge of c M < 1 string theory at zero cosmological constant. We systematically study the physical state spectrum of this topological sigma model and recover the spectrum in the absolute cohomology of c M < 1 string theory. This procedure provides us a manifestly topological representation of the continuum Liouville formulation of c M < 1 string theory.