Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2005-02-28
Phys.Rev. D71 (2005) 124023
Physics
High Energy Physics
High Energy Physics - Theory
41 pages, 3 eps figures, uses harvmac
Scientific paper
10.1103/PhysRevD.71.124023
We propose a phenomenological matrix model to study string theory in AdS_5 \times S_5 in the canonical ensemble. The model reproduces all the known qualitative features of the theory. In particular, it gives a simple effective potential description of Euclidean black hole nucleation and the tunnelling between thermal AdS and the big black hole. It also has some interesting predictions. We find that there exists a critical temperature at which the Euclidean small black hole undergoes a Gross-Witten phase transition. We identify the phase transition with the Horowitz-Polchinski point where the black hole horizon size becomes comparable to the string scale. The appearance of the Hagedorn divergence of thermal AdS is due to the merger of saddle points corresponding to the Euclidean small black hole and thermal AdS. The merger can be described in terms of a cusp (A_3) catastrophe and divergences at the perturbative string level are smoothed out at finite string coupling using standard techniques of catastrophe theory.
Alvarez-Gaume Luis
Gómez César
Liu Hong
Wadia Spenta
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