Numerical simulation of the N=(2,2) Landau-Ginzburg model

The two-dimensional 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 N=(2,2) superconformal field theory (SCFT) in the infrared (IR), the A2 model. From a finite-size scaling analysis of the susceptibility of the scalar field in the WZ model, we determine 1−h−h¯=0.616(25)(13) for the conformal dimensions h and h¯, while 1−h−h¯=0.666… for the A2 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 A2 model). These results are consistent with the conjectured emergence of the A2 model, and at the same time demonstrate that numerical studies can be complementary to analytical investigations for this two-dimensional supersymmetric field theory.