This talk will give a pedagogical account of the role played by integrability and instantons in N=2 SUSY gauge theories leading to recent understanding of what it means to quantize the integrable system.

N=4 SYM is known to have a confinement-deconfinement type phase transition in finite volume as the temperature is raised. This phase transition has been conjectured to smoothly become the Hawking-Page transition between hot AdS space and an AdS black hole as the 't Hooft coupling becomes larger. I show that this phase transition at weak coupling is actually a topology changing transition for the VEVs of the scalar fields and Polyakov loop. This means that the high temperature phase cannot be, as previously thought, the black hole in the dual. I then argue for the existence of a new second order phase transition at a higher temperature to a new phase which has the right symmetries to be identified with the black hole. This is work based on the recent paper hep-th/0703100 with Umut Gursoy, Sean Hartnoll and Prem Kumar.

D-branes are considered by the general particle physics community as the arcane inventions of the initiated having no relevance to even semi-realistic QFTs. In this seminar I want to provide compelling evidence that the domain walls of the simplest supersymmetric extension of QCD are D-branes for the confining string of the theory. Conventional D-brane technology then leads to a very intriguing result for the forces between the domain walls which suggests some underlying but unknown magic is at work. (based on hep-th/0505213,0601150)