The Hagedorn temperature in a decoupled sector of AdS/CFT
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.
Cite
@article{arxiv.hep-th/0701088,
title = {The Hagedorn temperature in a decoupled sector of AdS/CFT},
author = {Troels Harmark and Kristjan R. Kristjansson and Marta Orselli},
journal= {arXiv preprint arXiv:hep-th/0701088},
year = {2008}
}
Comments
7 pages. Talk presented by MO at the RTN workshop, Napoli, Oct. 9-13, 2007