# Continuum limit in numerical simulations of the $\mathcal{N}=2$ Landau--Ginzburg model

## TL;DR

This paper investigates the continuum limit of the two-dimensional $
=2$ Landau-Ginzburg model using lattice simulations, providing precise measurements of scaling dimensions and exploring the conjectured correspondence with superconformal field theories.

## Contribution

It introduces an extrapolation method to reach the continuum limit and employs a supersymmetric-invariant algorithm for accurate scaling dimension measurements.

## Key findings

- Successful continuum extrapolation of the model.
- Precise measurement of the scaling dimension.
- Support for the conjectured superconformal correspondence.

## Abstract

The $\mathcal{N}=2$ Landau--Ginzburg description provides a strongly interacting Lagrangian realization of an $\mathcal{N}=2$ superconformal field theory. It is conjectured that one such example is given by the two-dimensional $\mathcal{N}=2$ Wess--Zumino model. Recently, the conjectured correspondence has been studied by using numerical techniques based on lattice field theory; the scaling dimension and the central charge have been directly measured. We study a single superfield with a cubic superpotential, and give an extrapolation method to the continuum limit. Then, on the basis of a supersymmetric-invariant numerical algorithm, we perform a precision measurement of the scaling dimension through a finite-size scaling analysis.