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We study a discretization of ${\cal N}=2$ super Yang-Mills theory whichpossesses a single exact supersymmetry at non-zero lattice spacing. Thissupersymmetry arises after a reformulation of the theory in terms of {\ittwisted} fields. In this paper we derive the action of the other twistedsupersymmetries on the component fields and study, using Monte Carlosimulation, a series of corresponding Ward identities. Our results for SU(2)and SU(3) support a restoration of these additional supersymmetries withoutfine tuning in the infinite volume continuum limit. Additionally we presentevidence supporting a restoration of (twisted) rotational invariance in thesame limit. Finally we have examined the distribution of scalar fieldeigenvalues and find evidence for power law tails extending out to largeeigenvalue. We argue that these tails indicate that the classical moduli spacedoes not survive in the quantum theory.Comment: 35 pages, 14 figures, 18 tables. Results section rewritten to include  discussion of phase quenching, continuum scaling and thermal boundary  conditions. Version to be published in JHE

On the restoration of supersymmetry in twisted two-dimensional lattice Yang–Mills theory