Lectures on localization and matrix models in supersymmetric Chern-Simons-matter theories

TL;DR

This paper reviews recent advances in supersymmetric Chern-Simons-matter theories, focusing on localization and matrix models to derive exact results like the free energy behavior of ABJM theory on the three-sphere.

Contribution

It provides a pedagogical derivation of the exact interpolating function for ABJM free energy using localization and matrix model techniques.

Findings

Derivation of the N^{3/2} scaling of free energy at strong coupling

Explanation of localization and matrix model methods in supersymmetric theories

Connection between holographic renormalization and matrix models

Abstract

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