A Relation Between Approaches to Integrability in Superconformal Yang-Mills Theory

TL;DR

This paper explores the connection between the integrable structures of superstring theory on AdS5xS5 and the superconformal gauge theory, revealing a shared infinite-dimensional symmetry algebra and its implications for the planar limit.

Contribution

It establishes a link between the non-local symmetry of superstring theory and a non-abelian symmetry algebra in gauge theory, clarifying the integrability structure in the weakly coupled regime.

Findings

The planar one-loop dilatation operator acts as a spin chain Hamiltonian.

The dilatation operator commutes with non-abelian charges in the weak coupling limit.

A correspondence between string symmetries and gauge theory integrability is demonstrated.

Abstract

We make contact between the infinite-dimensional non-local symmetry of the typeIIB superstring on AdS5xS5 worldsheet theory and a non-abelian infinite-dimensional symmetry algebra for the weakly coupled superconformal gauge theory. We explain why the planar limit of the one-loop dilatation operator is the Hamiltonian of a spin chain, and show that it commutes with the g*2 N = 0 limit of the non-abelian charges.