Supersymmetric localization
Supersymmetric localization is a method to exactly compute correlation functions of supersymmetric operators in certain supersymmetric quantum field theories such as the partition function, supersymmetric Wilson loops, etc. The method can be seen as an extension of the Berline-Vergne-Atiyah-Bott formula for equivariant integration to path integrals of certain supersymmetric quantum field theories. Although the method cannot be applied to general local operators, it does provide the full nonperturbative answer for the restricted class of supersymmetric operators. It is a powerful tool which is currently extensively used in the study of supersymmetric quantum field theory. Applications range from the proof of the Erickson-Semenoff-Zarembo and Drukker-Gross conjecture by Vasily Pestun, which was the main motivation for the introduction of this technique building on previous work by Edward Witten, to the check of various dualities, and precision tests of the AdS/CFT correspondence.
