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

TL;DR

This study numerically investigates the IR behavior of the 2D $ abla=2$ Wess--Zumino model, confirming its correspondence to $ abla=2$ superconformal field theories and demonstrating a computational approach for correlation functions.

Contribution

It provides numerical evidence supporting the Landau--Ginzburg description of $ abla=2$ superconformal field theories and introduces a method to compute correlation functions in this context.

Findings

Scaling dimensions match $A_2$ and $A_3$ minimal models.

Central charges are consistent with superconformal field theories.

Supports the LG description of $ abla=2$ SCFTs.

Abstract

It is believed that the two-dimensional massless $\mathcal{N}=2$ Wess--Zumino model becomes the $\mathcal{N}=2$ superconformal field theory (SCFT) in the infrared (IR) limit. We examine this theoretical conjecture of the Landau--Ginzburg (LG) description of the $\mathcal{N}=2$ SCFT by numerical simulations on the basis of a supersymmetric-invariant momentum-cutoff regularization. We study a single supermultiplet with cubic and quartic superpotentials. From two-point correlation functions in the IR region, we measure the scaling dimension and the central charge, which are consistent with the conjectured LG description of the $A_2$ and $A_3$ minimal models, respectively. Our result supports the theoretical conjecture and, at the same time, indicates a possible computational method of correlation functions in the $\mathcal{N}=2$ SCFT from the LG description.