Two-dimensional N=(0,2) supersymmetry (2D $\mathcal{N}=(0,2)$ SUSY)

Two-dimensional $\mathcal{N}=(0,2)$ supersymmetry retains one complex right-moving supercharge. Its basic matter multiplets are chiral superfields containing a scalar and right-moving fermion, and Fermi superfields containing a left-moving fermion and an auxiliary scalar.

A Fermi superfield ${\Lambda }_{-}^a$ obeys ${\bar{D}}_{+}{\Lambda }_{-}^a=f_a(\Phi )$. A supersymmetric $J$-type coupling $\int d{\theta }^{+}{\Lambda }_{-}^a{J}^a(\Phi )$ requires ${\sum }_a{f}_a{J}^a=0$.