The Hagedorn temperature in a decoupled sector of AdS/CFT

TL;DR

This paper establishes a precise match between the Hagedorn/deconfinement temperature of planar N=4 SYM and string theory on AdS_5 x S^5 in a specific weakly coupled decoupling limit, linking gauge theory thermodynamics to spin chain models.

Contribution

It demonstrates the exact correspondence of Hagedorn temperatures in gauge and string theories within a decoupling limit, connecting SYM thermodynamics to the Heisenberg spin chain.

Findings

Hagedorn temperature matches between gauge and string theory in the decoupling limit.

The gauge theory thermodynamics relate to the Heisenberg spin chain.

Agreement of string and gauge theory Hagedorn temperatures in the near-critical regime.

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.