Finite-temperature phase diagram of the BMN matrix model on the lattice

TL;DR

This study uses lattice Monte Carlo simulations to map the finite-temperature phase diagram of the BMN matrix model, revealing a transition from first-order to continuous as coupling weakens.

Contribution

First non-perturbative lattice investigation of the BMN matrix model's thermal phase structure across a wide coupling range.

Findings

Deconfinement temperature matches perturbative and supergravity predictions.

Phase transition is first order at strong coupling.

Transition appears continuous at weaker couplings.

Abstract

We investigate the thermal phase structure of the Berenstein--Maldacena--Nastase (BMN) matrix model using non-perturbative lattice Monte Carlo calculations. Our main analyses span three orders of magnitude in the coupling, involving systems with sizes up to $N_{\tau} = 24$ lattice sites and SU($N$) gauge groups with $8 \leq N \leq 16$. In addition, we carry out extended checks of discretization artifacts for $N_{\tau} \leq 128$ and gauge group SU(4). We find results for the deconfinement temperature that interpolate between the perturbative prediction at weak coupling and the large-$N$ dual supergravity calculation at strong coupling. While we confirm that the phase transition is first order for strong coupling, it appears to be continuous for weaker couplings.