# Numerical study of ADE-type $\mathcal{N}=2$ Landau--Ginzburg models

## TL;DR

This paper numerically investigates the conjectured equivalence between two-dimensional $
=2$ Landau-Ginzburg models and superconformal field theories, confirming the LG/SCFT correspondence through precise measurements of central charge and scaling dimensions.

## Contribution

It introduces a numerical approach to test the LG/SCFT conjecture by measuring central charges and scaling dimensions in ADE-type models using supersymmetric-invariant regularization.

## Key findings

- Measured the central charge of ADE minimal models.
- Developed a method for continuum limit extrapolation.
- Results support the LG/SCFT correspondence.

## Abstract

At an extremely low-energy scale, it is believed that the two-dimensional $\mathcal{N}=2$ Wess--Zumino model becomes an $\mathcal{N}=2$ superconformal field theory (SCFT). We study this theoretical conjecture of the Landau--Ginzburg (LG) description by numerical simulations based on a supersymmetric-invariant momentum-cutoff regularization. First, from the two-point function of the energy-momentum tensor, we measure the central charge of the ADE minimal models. Second, we develop a method to take the continuum limit, and perform a precision measurement of the scaling dimension in the $A$-type minimal model. All our results show a coherence picture being consistent with the conjectured LG/SCFT correspondence.