Matching the Hagedorn temperature in 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. The near-critical region is near a point with zero temperature and critical chemical potential. 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 and we use this to compute it in two distinct regimes. On the string theory side, we identify the dual limit for which the string tension and string coupling go to zero. This limit is taken of string theory on a maximally supersymmetric 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.

32 pages, 1 figure. v2: Improvements in the discussion of the Penrose limit in sec. 6, typos fixed, ref. fixed. v3: Refs. added. v4: Typos fixed, footnote added

References in corpus (3)

• Phase Diagram of N=4 Super-Yang-Mills Theory with R-Symmetry Chemical Potentials
• Blackhole/String Transition for the Small Schwarzschild Blackhole of $Ad{S}_5\times S^5$ and Critical Unitary Matrix Models
• Quantum Mechanical Sectors in Thermal N=4 Super Yang-Mills on RxS^3

Cited by in corpus (14)

• Ferromagnetic behaviour in the strongly interacting two-component Bose gas
• Phase Transitions of Large N Orbifold Gauge Theories
• Decoupling limits of N=4 super Yang-Mills on R x S^3
• Warped AdS_5 Black Holes and Dual CFTs
• Confinement/Deconfinement Transition of Large N Gauge Theories in Perturbation Theory with N_f Fundamentals: N_f/N Finite
• Thermodynamics of theories with sixteen supercharges in non-trivial vacua
• Phase Transitions of Charged Kerr-AdS Black Holes from Large-N Gauge Theories
• Thermal N = 4 SYM theory as a 2D Coulomb gas
• Statistical mechanics for dilatations in N=4 super Yang--Mills theory
• Phases of Thermal N=2 Quiver Gauge Theories
• QCD Cosmology from the Lattice Equation of State
• Phase Structure of Beta-deformed N=4 SYM on S^3 with Chemical Potentials
• The Hagedorn temperature in a decoupled sector of AdS/CFT
• Lectures On AdS-CFT At Weak 't Hooft Coupling At Finite Temperature