Deconstruction, 2d lattice super-Yang-Mills, and the dynamical lattice spacing

We study expectation values related to the dynamical lattice spacing that occurs in the recent 2d lattice super-Yang-Mills constructions of Cohen et al. [hep-lat/0307012]. The corresponding observable in the fully-quenched ensemble would appear to indicate a difficulty with the proposed continuum limit. However, we find that the same observable in the phase-quenched ensemble takes a very different, perhaps encouraging, average value. Unfortunately, we are not able to obtain results for the full theory, due to the nearly flat distribution of the complex phase of the fermion determinant in the phase-quenched ensemble.