Non-positive fermion determinants in lattice supersymmetry

Details Non-positive fermion determinants in lattice supersymmetry Non-positive fermion determinants in lattice supersymmetry

2003-04-10

arxiv.org/abs/hep-lat/0304006v5

Nucl.Phys. B668 (2003) 138-150

Physics

High Energy Physics

High Energy Physics - Lattice

1+17 pages, 5 encapsulated figures, citations improved, comments added, prettier plots

Scientific paper

10.1016/j.nuclphysb.2003.07.006

We find that fermion determinants are not generally positive in a recent class of constructions with explicit lattice supersymmetry. These involve an orbifold of supersymmetric matrix models, and have as their target (continuum) theory (2,2) 2-dimensional super-Yang-Mills. The fermion determinant is shown to be identically zero for all boson configurations due to the existence of a zeromode fermion inherited from the "mother theory." Once this eigenvalue is factored out, the fermion determinant generically has arbitrary complex phase. We discuss the implications of this result for simulation of the models.

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