Numerical study of the $\mathcal{N}=2$ Landau--Ginzburg model with two superfields

TL;DR

This paper numerically investigates the low-energy limit of a two-dimensional $ abla=2$ Landau--Ginzburg model with two superfields, confirming its superconformal field theory nature and matching central charge predictions.

Contribution

It introduces a supersymmetric-invariant non-perturbative simulation method for the LG model with two superfields, extending previous studies to new minimal models.

Findings

Numerically determined central charges match theoretical predictions.

Confirmed the superconformal nature of the models studied.

Extended the numerical analysis to $D_3$, $D_4$, and $E_7$ models.

Abstract

In the low energy limit, the two-dimensional massless $\mathcal{N}=2$ Wess--Zumino (WZ) model with a quasi-homogeneous superpotential is believed to become a superconformal field theory. This conjecture of the Landau--Ginzburg (LG) description has been studied numerically in the case of the $A_2$, $A_3$, and $E_6$ minimal models. In this paper, by using a supersymmetric-invariant non-perturbative formulation, we simulate the WZ model with two superfields corresponding to the $D_3$, $D_4$, and $E_7$ models. Then, we numerically determine the central charge, and obtain the results that are consistent with the conjectured correspondence. We hope that this numerical approach, when further developed, will be useful to investigate superstring theory via the LG/Calabi--Yau correspondence.