The Hagedorn temperature in a decoupled sector of AdS/CFT

We match the Hagedorn/deconfinement temperature of planar N=4 super Yang-Mills (SYM) on R x S3 to the Hagedorn temperature of string theory on Ads5 x S5. 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 in which the physics of planar N=4 SYM is given exactly by the ferromagnetic XXX1/2 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 Ads5 x S5. 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 XXX1/2 Heisenberg spin chain with an external magnetic field. (Abstract Copyright [2007], Wiley Periodicals, Inc.)