Can the Hagedorn Phase Transition be explained from Matrix Model for Strings?

TL;DR

This paper investigates phase transitions in the BFSS matrix model, demonstrating a Hagedorn-like transition between membrane and D0-brane configurations, supported by both perturbative analysis and supergravity considerations.

Contribution

It provides a detailed analysis of phase transitions in the BFSS matrix model, linking perturbative results with supergravity insights and identifying a Hagedorn phase transition.

Findings

Existence of phase transition between membrane and D0-brane configurations

Hagedorn-like transition confirmed in supergravity context

Identification of a second phase transition similar to Gregory-Laflamme instability

Abstract

The partition function of BFSS matrix model is studied for two different classical backgrounds upto 1-loop level. One of the backgrounds correspond to a membrane wrapped around a compact direction and another to a localized cluster of $D0$-branes. It is shown there exist phase transitions between these two configurations - but only in presence of an IR cut-off. The low temperature phase corresponds to a string (wrapped membrane) phase and so we call this the Hagedorn phase transition. While the presence of an IR cut-off seemingly is only required for perturbative analysis to be valid, the physical necessity of such a cut-off can be seen in the dual supergravity side. It has been argued from entropy considerations that a finite size horizon must develop even in an extremal configuration of D0-branes, from higher derivative $O(g_s)$ corrections to supergravity. It can then be shown that the Hagedorn like transition exists in supergravity also. Interestingly the perturbative analysis also shows a second phase transition back to a string phase. This is also reminiscent of the Gregory-Laflamme instability.