Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-01-10
Fortsch.Phys.55:754-759,2007
Physics
High Energy Physics
High Energy Physics - Theory
7 pages. Talk presented by MO at the RTN workshop, Napoli, Oct. 9-13, 2007
Scientific paper
10.1002/prop.200610360
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.
Harmark Troels
Kristjansson Kristjan R.
Orselli Marta
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