Integrable gauge theories at finite temperature

We propose a project to explore the properties of supersymmetric gauge theories at finite temperature, with special emphasis on those that are integrable in the large N limit. In particular we study the de-confinement of these theories using the newest integrability methods which have recently proved to be a powerful tool in finding the Hagedorn temperature as a function of the theory's coupling. Progress in this field can lead to better understanding of the long unsolved problem of confinement in gauge theories and the de-confinement of confining theories such as QCD at finite temperature. The project will also investigate string theories on curved space with background fields. The results of the Hagedorn temperature at strong coupling provide sharp predictions for how the string theory duals should behave, but showing it directly has so far proved elusive. The project will use the results for the Hagedorn temperature and its higher order effects to as a guide-post to determine the correct world-sheet structure for both type IIB and IIA string theories on AdS spaces. Uppsala University has been a world leader in developing techniques for exploring supersymmetric gauge theories, including integrability and localization, which have led to powerful results. The project would fund a total of five post-doc positions and two graduate students over the five year period to investigate these questions, providing excellent scientific opportunities for young theoretical physicists.