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

TL;DR

This study uses lattice simulations with a Nicolai map to investigate the N=2 Landau-Ginzburg model, providing numerical evidence supporting its conjectured relation to superconformal minimal models.

Contribution

It introduces a lattice approach employing the Nicolai map to analyze the N=2 Landau-Ginzburg model and measures conformal weights at the IR fixed point.

Findings

Conformal weight (h,  h) = (1/6, 1/6) within error margins.

Numerical result for 1 -  h consistent with theoretical predictions.

Systematic errors estimated to be less than 0.5%.

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 %.