Numerical simulation of the $\mathcal{N}=(2,2)$ Landau-Ginzburg model

TL;DR

This paper numerically investigates the two-dimensional $ N=(2,2)$ Landau-Ginzburg model with a cubic superpotential, confirming its flow to the $A_2$ superconformal field theory through finite-size scaling and correlation function analysis.

Contribution

It introduces a supersymmetry-preserving momentum-cutoff regularization and a Nicolai map-based algorithm to numerically study the model's IR behavior.

Findings

Determined conformal dimensions consistent with the $A_2$ model.

Measured the central charge close to the theoretical value.

Confirmed the IR flow to the $ N=(2,2)$ superconformal field theory.

Abstract

The two-dimensional $\mathcal{N}=(2,2)$ Wess-Zumino (WZ) model with a cubic superpotential is numerically studied with a momentum-cutoff regularization that preserves supersymmetry. A numerical algorithm based on the Nicolai map is employed and the resulting configurations have no autocorrelation. This system is believed to flow to an $\mathcal{N}=(2,2)$ superconformal field theory (SCFT) in the infrared (IR), the $A_2$ model. From a finite-size scaling analysis of the susceptibility of the scalar field in the WZ model, we determine $1-h-\Bar{h}=0.616(25)(13)$ for the conformal dimensions $h$ and $\Bar{h}$, while $1-h-\Bar{h}=0.666...$ for the $A_2$ model. We also measure the central charge in the IR region from a correlation function between conserved supercurrents and obtain $c=1.09(14)(31)$ ($c=1$ for the $A_2$ model). These results are consistent with the conjectured emergence of the $A_2$ model, and at the same time demonstrate that numerical studies can be complementary to analytical investigations for this two-dimensional supersymmetric field theory.