Can the Hagedorn phase transition be explained from matrix model for strings?

Abstract

The partition function of BFSS matrix model is studied for two different classical backgrounds up to 1-loop level. One of the backgrounds correspond to a membrane wrapped around a compact direction and another to a localised cluster of D0-branes. It is shown that, 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 super-gravity 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(gs) corrections to super-gravity. It can then be shown that the Hagedorn like transition exists in super-gravity also. Interestingly the perturbative analysis also shows a second phase transition back to a string phase. This is reminiscent of the Gregory-Laflamme instability.