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

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.

35 pages, 37 figures, the final version to appear PTEP

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• Low-dimensional Supersymmetric Lattice Models
• Two-Dimensional Wess-Zumino Models at Intermediate Couplings
• Taming the Leibniz Rule on the Lattice
• A lattice study of N=2 Landau-Ginzburg model using a Nicolai map
• Supersymmetry restoration in lattice formulations of 2D $\mathcal{N}=(2,2)$ WZ model based on the Nicolai map
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Cited by in corpus (4)

• Lectures on 4d N=1 dynamics and related topics
• 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