Abstract
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.
| Original language | English |
|---|---|
| Journal | Fortschritte der Physik |
| Volume | 55 |
| Issue number | 5-7 |
| Pages (from-to) | 754-759 |
| Number of pages | 6 |
| ISSN | 0015-8208 |
| DOIs | |
| Publication status | Published - 1 May 2007 |
Keywords
- AdS/CPT correspondence
- Finite temperature gauge theories
- Strings on a pp-wave background