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arXiv · hep-th/0701088

The Hagedorn temperature in a decoupled sector of AdS/CFT

Troels Harmark·Kristjan R. Kristjansson·Marta Orselli
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Abstract

We match the Hagedorn/deconfinement temperature of planar N=4 super Yang-Mills (SYM) on R x S^3 to the Hagedorn temperature of string theory on AdS_5 x S^5. The match is done in a near-critical region where both gauge theory and string theory are weakly coupled. On the gauge theory side we are taking a decoupling limit found in hep-th/0605234 in which the physics of planar N=4 SYM is given exactly by the ferromagnetic XXX_{1/2} Heisenberg spin chain. We find moreover a general relation between the Hagedorn/deconfinement temperature and the thermodynamics of the Heisenberg spin chain. On the string theory side, we identify the dual limit which is taken of string theory on a maximally symmetric pp-wave background with a flat direction, obtained from a Penrose limit of AdS_5 x S^5. We compute the Hagedorn temperature of the string theory and find agreement with the Hagedorn/deconfinement temperature computed on the gauge theory side. Finally, we discuss a modified decoupling limit in which planar N=4 SYM reduces to the XXX_{1/2} Heisenberg spin chain with an external magnetic field.

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Troels Harmark, Kristjan R. Kristjansson, Marta Orselli. 2007-12-06. The Hagedorn temperature in a decoupled sector of AdS/CFT. https://doi.org/10.1002/prop.200610360

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