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arXiv · 0805.0076

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

B. Sathiapalan·Nilanjan Sircar
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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.

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B. Sathiapalan, Nilanjan Sircar. 2008-07-17. Can the Hagedorn Phase Transition be explained from Matrix Model for Strings?. https://doi.org/10.1088/1126-6708%2F2008%2F08%2F019

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