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.
On the sign problem in 2D lattice super Yang--Mills
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abstract
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.