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Lectures on localization and matrix models in supersymmetric Chern-Simons-matter theories. (English) Zbl 1270.81235

Summary: In these lectures, I give a pedagogical presentation of some of the recent progress in supersymmetric Chern-Simons-matter theories, coming from the use of localization and matrix model techniques. The goal is to provide a simple derivation of the exact interpolating function for the free energy of ABJM theory on the three-sphere, which implies in particular the \(N^{3/2}\) behavior at strong coupling. I explain in detail part of the background needed to understand this derivation, like holographic renormalization, localization of path integrals and large \(N\) techniques in matrix models.

MSC:

81V22 Unified quantum theories
81-02 Research exposition (monographs, survey articles) pertaining to quantum theory
81T60 Supersymmetric field theories in quantum mechanics
81T10 Model quantum field theories
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81V17 Gravitational interaction in quantum theory