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Integrable Systems in Gauge and String Theory

Mid-Term Report Summary - INTEGRAL (Integrable Systems in Gauge and String Theory)

The term "holographic duality" refers to a remarkable relationship between gauge fields, string theory and quantum gravity, discovered in 1997. It appeared that strongly coupled quantum fields may have an alternative, and simpler description in terms of classical gravity in a curved space of one dimension higher.
The holographic duality has become one of the major lines of research in theoretical physics. And yet its consequences remain largely unexplored, especially when it comes to reliable, systematic calculations from first principles. The aim of this project is to develop and use advanced mathematical tools to study holographic duality, with emphasis on exact results.

One major strand of this project is to explore an interplay of holography and localization, a method to calculate path integrals in quantum field theory without approximations. Spectacular tests of the holographic duality, which are unique in the case of the theories with a mass gap, have been performed with the help of localization during the course of the project. Another strand is the use of integrable systems to study holography. Novel methods developed here substantially extended our knowledge of the inner workings of holography. The use of integrability has been extended to so far unexplored domains, such as models with reduced dimension, or to theories with space-time defects.