Exact results for supersymmetric quantum mechanics on the lattice

Abstract

We discuss N=2 supersymmetric quantum mechanics on the lattice using the fermion loop formulation. In this approach the system naturally decomposes into a bosonic and fermionic sector. This allows us to deal with the sign problem arising in the context of broken supersymmetry due to the vanishing of the Witten index. Employing transfer matrix techniques we obtain exact results at finite lattice spacing and are hence able to study how the continuum limit is approached. In particular, we determine how supersymmetry is restored and how, in the case of broken supersymmetry, the goldstino mode emerges.