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On the sign problem in 2D lattice super Yang--Mills
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In recent years a new class of supersymmetric lattice theories have been proposed which retain one or more exact supersymmetries for non-zero lattice spacing. Recently there has been some controversy in the literature concerning whether these theories suffer from a sign problem. In this paper we address this issue by conducting simulations of the N=(2, 2) and N=(8, 8) supersymmetric Yang--Mills theories in two dimensions for the U(N) theories with N=2,3,4, using the new twisted lattice formulations. Our results provide evidence that these theories do not suffer from a sign problem in the continuum limit. These results thus boost confidence that the new lattice formulations can be used successfully to explore non-perturbative aspects of four-dimensional N=4 supersymmetric Yang--Mills theory.
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Finite-temperature phase diagram of the BMN matrix model on the lattice
Non-perturbative lattice calculations determine the BMN deconfinement temperature from the perturbative to the holographic regime, with evidence that the transition becomes continuous at weak coupling.
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