Non-perturbative Field Theory

TL;DR

This paper discusses how integrable two-dimensional quantum field theory techniques enable exact solutions for four-dimensional N=4 gauge theory via the AdS/CFT correspondence, including precise anomalous dimension calculations.

Contribution

It introduces methods to exactly compute all anomalous dimensions in N=4 gauge theory using integrability and AdS/CFT, exemplified by the Konishi operator.

Findings

Exact anomalous dimensions for operators in N=4 gauge theory

Agreement between string theory and gauge theory calculations for Konishi operator

Application of integrable models to solve four-dimensional quantum field theories

Abstract

In this talk we review recent developments which enable us to use techniques of integrable two-dimensional quantum field theories to solve exactly four dimensional N=4 gauge theory through the use of the AdS/CFT correspondence. By `solve' we mean here to find all anomalous dimensions of all operators of the theory for any value of the gauge coupling. We illustrate the methods with the case of the Konishi operator, the simplest operator not protected by supersymmetry, whose perturbative anomalous dimension can be computed from the string side of the AdS/CFT correspondence and is in exact agreement with a direct gauge theory perturbative computation.