Large $N$ limits of supersymmetric quantum field theories: A pedagogical overview

TL;DR

This paper provides a comprehensive, pedagogical overview of large N limits in supersymmetric quantum field theories across various dimensions, focusing on exact sphere partition function calculations and their role in AdS/CFT correspondence.

Contribution

It offers a detailed, accessible explanation of solving sphere partition functions in different large N limits, including the saddle point method and numerous examples, for the first time in a unified manner.

Findings

Exact solutions for sphere partition functions in various large N limits

Pedagogical explanation of saddle point approximation techniques

Extensive list of examples demonstrating the methods

Abstract

The different large $N$ limits of supersymmetric quantum field theories in three, four, and five dimensions are reviewed. We distinguish between the planar limit of SQCD theories, the M-theory limit suited in three and five dimensions, and the long quiver limit. The method to solve exactly the sphere partition functions in each type of limit is spelled out in a pedagogical way. After a comprehensive general treatment of the saddle point approximation in the large $N$ limit, we present an extensive list of examples and detail the calculations. The scope of this overview is to provide an entry-level, computation-oriented understanding of the techniques featured in the field theory side of the AdS/CFT correspondence.