Topological First-Order Systems with Landau-Ginzburg Interactions

TL;DR

This paper develops a framework for realizing N=2 superconformal models using free first-order systems with Landau-Ginzburg interactions, enabling explicit calculations of topological correlators and connecting to known minimal models.

Contribution

It introduces a method to incorporate Landau-Ginzburg interactions into superconformal models without losing invariance, and provides explicit calculation techniques for topological correlators.

Findings

Parameters in the potential are flat coordinates.

Explicit power series calculations of correlators are possible.

Results recover known minimal model and torus correlators.

Abstract

We consider the realization of N=2 superconformal models in terms of free first-order $(b,c,\beta,\gamma)$-systems, and show that an arbitrary Landau-Ginzburg interaction with quasi-homogeneous potential can be introduced without spoiling the (2,2)-superconformal invariance. We discuss the topological twisting and the renormalization group properties of these theories, and compare them to the conventional topological Landau-Ginzburg models. We show that in our formulation the parameters multiplying deformation terms in the potential are flat coordinates. After properly bosonizing the first-order systems, we are able to make explicit calculations of topological correlation functions as power series in these flat coordinates by using standard Coulomb gas techniques. We retrieve known results for the minimal models and for the torus.