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We present a simple lattice formulation of two-dimensional$\mathcal{N}=(2,2)$ $U(k)$ supersymmetric QCD (SQCD) with $N$ matter multipletsin the fundamental representation. The construction uses compact gauge linkvariables and exactly preserves one linear combination of supercharges on thetwo-dimensional regular lattice. Artificial saddle points in the weak couplinglimit and the species doubling are evaded without imposing the admissibility. Aperturbative power-counting argument indicates that the target supersymmetrictheory is realized in the continuum limit without any fine tuning.

Lattice formulation of 2D $\mathcal{N}=(2,2)$ SQCD based on the B model twist