On the Landau-Ginzburg Description of $N=2$ Minimal Models

TL;DR

This paper tests the conjecture that two-dimensional $N=2$ minimal models can be described as critical points of a Landau-Ginzburg theory, providing computational evidence and algebraic support for this Landau-Ginzburg/$N=2$ minimal model correspondence.

Contribution

It offers a path integral computation approach and algebraic analysis to support the Landau-Ginzburg description of $N=2$ minimal models.

Findings

Derived simple character expressions for $N=2$ models from Landau-Ginzburg path integrals.

Verified character expressions at low levels.

Found $N=2$ superconformal algebra within noncritical Landau-Ginzburg systems.

Abstract

The conjecture that $N=2$ minimal models in two dimensions are critical points of a super-renormalizable Landau-Ginzburg model can be tested by computing the path integral of the Landau-Ginzburg model with certain twisted boundary conditions. This leads to simple expressions for certain characters of the $N=2$ models which can be verified at least at low levels. An $N=2$ superconformal algebra can in fact be found directly in the {\it noncritical} Landau-Ginzburg system, giving further support for the conjecture.