Non-positive fermion determinants in lattice supersymmetry

TL;DR

This paper demonstrates that in certain lattice supersymmetry models, fermion determinants are often non-positive and can have complex phases, complicating numerical simulations.

Contribution

It reveals the presence of zero modes causing the fermion determinant to be zero and shows that, after removing these, the determinant generally acquires a complex phase.

Findings

Fermion determinants are identically zero for all boson configurations due to zero modes.

Removing zero modes leaves a determinant with an arbitrary complex phase.

Implications for simulation methods of lattice supersymmetric models are discussed.

Abstract

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.