A lattice study of N=2 Landau-Ginzburg model using a Nicolai map

Abstract

It has been conjectured that the two-dimensional N=2 Wess-Zumino model with a quasi-homogeneous superpotential provides the Landau-Ginzburg description of the N=2 superconformal minimal models. For the cubic superpotential W=(lambda) Phi^3/3, it is expected that the Wess-Zumino model describes A_{2} model and the chiral superfield Phi shows the conformal weight (h,bar{h})=(1/6,1/6) at the IR fixed point. We study this conjecture by a lattice simulation, extracting the weight from the finite volume scaling of the susceptibility of the scalar component in Phi. We adopt a lattice model with the overlap fermion, which possesses a Nicolai map and a discrete R-symmetry. We set a(lambda)=0.3 and generate the scalar field configurations by solving the Nicolai map on L times L lattices in the range L=18 - 32. To solve the map, we use the Newton-Raphson algorithm with various initial configurations. The result is 1-h-bar{h}=0.660 \pm0.011, which is consistent with the conjecture within the statistical error, while a systematic error is estimated as less than 0.5 %.

arXiv comment10 pages, 1 figures, references added, minor text corrections

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Cited by in corpus (12)

• Supersymmetric Yang-Mills Theories: not quite the usual perspective
• 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
• Direct computational approach to lattice supersymmetric quantum mechanics
• Lectures on 4d N=1 dynamics and related topics
• Numerical simulation of the $\mathcal{N}=(2,2)$ Landau-Ginzburg model
• 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
• Witten index from lattice simulation
• Numerical study of ADE-type $\mathcal{N}=2$ Landau--Ginzburg models