Matching the Hagedorn temperature in AdS/CFT

by Harmark, Troels (NBI Copenhagen)

Tuesday 27 Mar 2007, 14:00 → 15:00 Europe/Zurich

TH Auditorium (CERN)

We match the Hagedorn temperature, as computed in planar N=4 super Yang-Mills theory on R x S³, with the Hagedorn temperature computed in a pp-wave limit of string theory on AdS₅ x S⁵. This is done in a certain decoupling limit in which the planar super Yang-Mills theory can be described by the ferromagnetic XXX_1/2 Heisenberg spin chain. On the string side the decoupling limit is taken on the spectrum of the pp-wave. In this way we are able to find the same spectrum and thereby the same Hagedorn temperature from the gauge theory and string theory sides. Moreover, by using a general relation between the spin chain free energy and the Hagedorn temperature we can connect the Hagedorn temperature computed in weakly-coupled gauge theory with that computed in string theory.