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Recently a class of supersymmetric gauge theories have been successfullyimplemented on the lattice. However, there has been an ongoing debate onwhether lattice versions of some of these theories suffer from a sign problem,with independent simulations for the ${\cal N} = (2, 2)$ supersymmetricYang-Mills theories in two dimensions yielding seemingly contradictory results.Here, we address this issue from an interesting theoretical point of view. Weconjecture that the sign problem observed in some of the simulations is relatedto the so called Neuberger 0/0 problem, which arises in ordinarynon-supersymmetric lattice gauge theories, and prevents the realization ofBecchi-Rouet-Stora-Tyutin symmetry on the lattice. After discussing why weexpect a sign problem in certain classes of supersymmetric lattice gaugetheories far from the continuum limit, we argue that these problems can beevaded by use of a non-compact parametrization of the gauge link fields.

Supersymmetric gauge theories on the lattice: Pfaffian phases and the Neuberger 0/0 problem