Non Scale-Invariant Topological Landau-Ginzburg Models

TL;DR

This paper explores a non scale-invariant Landau-Ginzburg approach to 2D topological sigma models, deriving quantum cohomology relations and explicitly computing correlation functions using a logarithmic superpotential.

Contribution

It introduces a non scale-invariant Landau-Ginzburg formulation for topological sigma models and explicitly evaluates correlation functions with a novel logarithmic superpotential.

Findings

Derivation of quantum cohomology relations from equations of motion

Explicit computation of topological correlation functions in specific models

Identification of a logarithmic superpotential characteristic of massive supersymmetric theories

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.