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 |