Non Scale-Invariant Topological Landau-Ginzburg Models

Abstract

The Landau-Ginzburg formulation of two-dimensional topological sigma models on the target space with positive first Chern class is considered. The effective Landau-Ginzburg superpotential takes the form of logarithmic type which is characteristic of supersymmetric theories with the mass gap. The equations of motion yield the defining relations of the quantum cohomology ring. Topological correlation functions in the $CP^{n-1}$ and Grassmannian models are explicitly evaluated with the use of the logarithmic superpotential.