The Hagedorn temperature in a decoupled sector of AdS/CFT

TY - JOUR

T1 - The Hagedorn temperature in a decoupled sector of AdS/CFT

AU - Harmark, Troels

AU - Kristjansson, Kristjan R.

AU - Orselli, Marta

PY - 2007/5/1

Y1 - 2007/5/1

N2 - We match the Hagedorn/deconfinement temperature of planar N = 4 super Yang-Mills (SYM) on ℝ × S3 to the Hagedorn temperature of string theory on AdS5 × 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 found in [7] 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 Hagedom/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 × 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.

AB - We match the Hagedorn/deconfinement temperature of planar N = 4 super Yang-Mills (SYM) on ℝ × S3 to the Hagedorn temperature of string theory on AdS5 × 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 found in [7] 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 Hagedom/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 × 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.

KW - AdS/CPT correspondence

KW - Finite temperature gauge theories

KW - Strings on a pp-wave background

U2 - 10.1002/prop.200610360

DO - 10.1002/prop.200610360

M3 - Journal article

AN - SCOPUS:34250376970

SN - 0015-8208

VL - 55

SP - 754

EP - 759

JO - Fortschritte der Physik

JF - Fortschritte der Physik

IS - 5-7

ER -