Free Energy and Phase Transition of the Matrix Model on a Plane-Wave

TL;DR

This paper investigates the phase transition in the plane wave matrix model at finite temperature, demonstrating it is of first order and calculating corrections to the Hagedorn temperature through three-loop effective potential analysis.

Contribution

It provides a detailed three-loop analysis of the effective potential, confirming the first-order nature of the phase transition and refining the Hagedorn temperature estimate.

Findings

The phase transition is confirmed to be of first order.

Interactions significantly influence the transition's nature.

Hagedorn temperature corrections are computed to two-loop order.

Abstract

It has recently been observed that the weakly coupled plane wave matrix model has a density of states which grows exponentially at high energy. This implies that the model has a phase transition. The transition appears to be of first order. However, its exact nature is sensitive to interactions. In this paper, we analyze the effect of interactions by computing the relevant parts of the effective potential for the Polyakov loop operator in the finite temperature plane-wave matrix model to three loop order. We show that the phase transition is indeed of first order. We also compute the correction to the Hagedorn temperature to order two loops.