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

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.

32 pages, 15 figures, the final version to appear in Nuclear Physics B

References in corpus (6)

• Low-dimensional Supersymmetric Lattice Models
• Two-Dimensional Wess-Zumino Models at Intermediate Couplings
• A lattice study of N=2 Landau-Ginzburg model using a Nicolai map
• A Method for Measuring the Witten Index Using Lattice Simulation
• Supersymmetry restoration in lattice formulations of 2D $\mathcal{N}=(2,2)$ WZ model based on the Nicolai map
• The two dimensional N=(2,2) Wess-Zumino Model in the Functional Renormalization Group Approach

Cited by in corpus (7)

• Direct computational approach to lattice supersymmetric quantum mechanics
• Lectures on 4d N=1 dynamics and related topics
• Lattice study of supersymmetry breaking in N=2 supersymmetric quantum mechanics
• Numerical study of the $\mathcal{N}=2$ Landau--Ginzburg model
• Continuum limit in numerical simulations of the $\mathcal{N}=2$ Landau--Ginzburg model
• Numerical study of the $\mathcal{N}=2$ Landau--Ginzburg model with two superfields
• Numerical study of ADE-type $\mathcal{N}=2$ Landau--Ginzburg models