HET Journal Club: Alexander Kristensson
Speaker: Alexander Kristensson
Title: Thermodynamics of N=4 SYM at finite N
Abstract: The maximally Supersymmetric Yang Mills (SYM) theory is an SU(N) gauge theory that occurs many places in theoretical high-energy physics -- most notably in the famous AdS/CFT duality. On a compact space RxS^3, N=4 SYM theory exhibits a phase transition similar to the confinement/deconfinement phase transition of Quantum Chromo Dynamics (QCD). On the gravity side of the duality, this phase transition is believed to be dual to the Hawking-Page phase transition between a gas of gravitons and a black hole. In the last twenty years, there has been much progress in understanding the planar limit of the theory, where one takes N -> infinity. This progress has shown strong hints of the theory being integrable. The main focus of our research is to push this understanding beyond the planar limit to finite values of N. In this talk I will present our ongoing research on the thermodynamics of N=4 SYM at finite N. In particular, I will discuss various sub-sectors of the full algebra and show how to compute the exact partition functions for small values of N. In the su(2) sector, I will present the claim that the Hagedorn behaviour at N -> infinity is replaced by a phase transition of Lee-Yang type at finite N, characterized by a condensation of zeros in the complex fugacity plane.