The fermion determinant in (4,4) 2d lattice super-Yang-Mills

We find that the fermion determinant is not generally positive in a class of lattice actions recently constructed by Cohen et al. [hep-lat/0307012]; these are actions that contain an exact lattice supersymmetry and have as their target (continuum) theory (4,4) 2-dimensional super-Yang-Mills. We discuss the implications of this finding for lattice simulations and give some preliminary results for the phase of the determinant in the phase-quenched ensemble