Two-dimensional N=(2,2) super Yang-Mills theory on computer

Understand

We carry out preliminary numerical study of Sugino's lattice formulation \cite{Sugino:2004qd,Sugino:2004qdf} of the two-dimensional $\mathcal{N}=(2,2)$ super Yang-Mills theory (2d $\mathcal{N}=(2,2)$ SYM) with the gauge group $\SU(2)$.

• The effect of dynamical fermions is included by re-weighting a quenched ensemble by the pfaffian factor.
• It appears that the complex phase of the pfaffian due to lattice artifacts and flat directions of the classical potential are not problematic in Monte Carlo simulation.
• Various one-point supersymmetric Ward-Takahashi (WT) identities are examined for lattice spacings up to $a=0.5/g$ with the fixed physical lattice size $L=4.0/g$, where $g$ denotes the gauge coupling constant in two dimensions.