Large N Limits of Supersymmetric Quantum Field Theories: A Pedagogical Overview

Abstract

The different large (Formula presented.) limits of supersymmetric quantum field theories in three, four, and five dimensions are reviewed. The author distinguishes 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 (Formula presented.) limit, the author also presents 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.