Critique of the link approach to exact lattice supersymmetry

We examine the link approach to constructing a lattice theory of $\mathcal{N}=2$ super Yang-Mills theory in two dimensions. The goal of this construction is to provide a discretization of the continuum theory which preserves all supersymmetries at nonzero lattice spacing. We show that this approach suffers from an inconsistency and argue that a maximum of just one of the supersymmetries can be implemented on the lattice.

Figure 1

Symmetric choice of shift parameter $a_A$ for twisted $\mathcal{N}=D=2$.