Abstract
We derive the fermion loop formulation of \( \mathcal{N}=4 \) supersymmetric SU(N) Yang-Mills quantum mechanics on the lattice. The loop formulation naturally separates the contributions to the partition function into its bosonic and fermionic parts with fixed fermion number and provides a way to control potential fermion sign problems arising in numerical simulations of the theory. Furthermore, we present a reduced fermion matrix determinant which allows the projection into the canonical sectors of the theory and hence constitutes an alternative approach to simulate the theory on the lattice.
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Steinhauer, K., Wenger, U. Loop formulation of supersymmetric Yang-Mills quantum mechanics. J. High Energ. Phys. 2014, 44 (2014). https://doi.org/10.1007/JHEP12(2014)044
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DOI: https://doi.org/10.1007/JHEP12(2014)044