Non-perturbative phase structure of the bosonic BMN matrix model

TL;DR

This study investigates the phase transitions of the bosonic BMN matrix model across various parameters using lattice computations, revealing a consistent first-order transition and analyzing how critical temperature varies with deformation.

Contribution

It provides the first non-perturbative analysis of the phase structure of the bosonic BMN matrix model over a wide parameter range using lattice methods.

Findings

Identified a single first-order phase transition across all parameters.

Characterized the dependence of critical temperature on deformation.

Interpolated results between bosonic BFSS and gauged Gaussian models.

Abstract

We study the bosonic part of the BMN matrix model for wide ranges of temperatures, values of the deformation parameter, and numbers of colors $16 \leq N \leq 48$. Using lattice computations, we analyze phase transitions in the model, observing a single first-order transition from a uniform to a gapped phase for all values of the deformation parameter. We study the functional form of the dependence of the critical temperature on the deformation parameter, to describe how our results smoothly interpolate between the limits of the bosonic BFSS model and the gauged Gaussian model.