Thermal phase structure of dimensionally reduced super-Yang--Mills

Abstract

We present our current results from ongoing lattice investigations of the Berenstein--Maldacena--Nastase deformation of maximally supersymmetric Yang--Mills quantum mechanics. We focus on the thermal phase structure of this theory, which depends on both the temperature $T$ and the deformation parameter $\mu$, through the dimensionless ratios $T/\mu$ and $g=\lambda /{\mu }^3$ with $\lambda$ the 't Hooft coupling. We determine the critical $T/\mu$ of the confinement transition for couplings $g$ that span three orders of magnitude, to connect weak-coupling perturbative calculations and large-$N$ dual supergravity predictions in the strong-coupling limit. Analyzing multiple lattice sizes up to $N_{\tau }=24$ and numbers of colors up to $N=16$ allows initial checks of the large-$N$ continuum limit.

arXiv commentContribution to the proceedings of Lattice 2021, July 26--30, MIT

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• Witten index of BMN matrix quantum mechanics
• Nonperturbative test of the Maldacena-Milekhin conjecture for the BMN matrix model
• Non-perturbative phase structure of the bosonic BMN matrix model