Supersymmetric quantum mechanics on the lattice: I. Loop formulation

Baumgartner, David; Wenger, Urs (2015). Supersymmetric quantum mechanics on the lattice: I. Loop formulation. Nuclear physics. B, 894, pp. 223-253. North Holland 10.1016/j.nuclphysb.2015.03.001

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Simulations of supersymmetric field theories on the lattice with (spontaneously) broken supersymmetry suffer from a fermion sign problem related to the vanishing of the Witten index. We propose a novel approach which solves this problem in low dimensions by formulating the path integral on the lattice in terms of fermion loops. For N=2 supersymmetric quantum mechanics the loop formulation becomes particularly simple and in this paper – the first in a series of three – we discuss in detail the reformulation of this model in terms of fermionic and bosonic bonds for various lattice discretisations including one which is Q-exact.

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