A strange relationship between 2d CFT and 4d gauge theory

TL;DR

This paper reviews the intriguing connection between 2D conformal field theory and 4D gauge theory, demonstrating explicit calculations and exploring string theory perspectives to understand their relationship.

Contribution

It provides a foundational review and explicit verification of the correspondence between 2D CFT and 4D gauge theory, including string theory insights.

Findings

Agreement between 2D CFT coherent state norm and 4D instanton partition function

Explicit calculations confirming the relationship

String and M theory perspectives elucidate the connection

Abstract

A relationship between 4d gauge theory and 2d CFT will be reviewed from the very basics. We will first cover the introductory material on the 2d CFT and on the instantons of 4d gauge theory. Next we will explicitly calculate and check the agreement of the norm of a coherent state on the 2d side and the instanton partition function on the 4d side. We will then see how this agreement can be understood from the perspective of string and M theory.