Dynamical aspects of the plane-wave matrix model at finite temperature

TL;DR

This paper investigates the finite-temperature behavior of the plane-wave matrix model, analyzing phase transitions, free energy, and gauge field configurations using both analytical and numerical methods, revealing fuzzy sphere phases and the trivial vacuum's dominance at high temperatures.

Contribution

It provides a detailed analysis of the phase structure and Hagedorn transition in the plane-wave matrix model at finite temperature, including new insights into fuzzy sphere phases and vacuum dominance.

Findings

Fuzzy sphere phases exist near the critical temperature.

The trivial vacuum has the lowest free energy at high temperature.

Analytic and Monte Carlo methods agree near the critical point.

Abstract

We study dynamical aspects of the plane-wave matrix model at finite temperature. One-loop calculation around general classical vacua is performed using the background field method, and the integration over the gauge field moduli is carried out both analytically and numerically. In addition to the trivial vacuum, which corresponds to a single M5-brane at zero temperature, we consider general static fuzzy-sphere type configurations. They are all 1/2 BPS, and hence degenerate at zero temperature due to supersymmetry. This degeneracy is resolved, however, at finite temperature, and we identify the configuration that gives the smallest free energy at each temperature. The Hagedorn transition in each vacuum is studied by using the eigenvalue density method for the gauge field moduli, and the free energy as well as the Polyakov line is obtained analytically near the critical point. This reveals the existence of fuzzy sphere phases, which may correspond to the plasma-ball phases in N=4 SU(\infty) SYM on S^1 X S^3. We also perform Monte Carlo simulation to integrate over the gauge field moduli. While this confirms the validity of the analytic results near the critical point, it also shows that the trivial vacuum gives the smallest free energy throughout the high temperature regime.