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

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.