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

It has been conjectured that the two-dimensional N=2 Wess-Zumino model with a quasihomogeneous superpotential provides the Landau-Ginzburg description of the N=2 superconformal minimal models. For the cubic superpotential W=λΦ3/3, it is expected that the Wess-Zumino model describes A2 model and the chiral superfield Φ shows the conformal weight (h,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 Φ. We adopt a lattice model with the overlap fermion, which possesses a Nicolai map and a discrete R-symmetry. We set aλ=0.3 and generate the scalar field configurations by solving the Nicolai map on LxL 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-h=0.660±0.011, which is consistent with the conjecture within the statistical error, while a systematic error is estimated as less than 0.5%.