Schur-Weyl duality as an instrument of Gauge-String duality

TL;DR

This paper explores how Schur-Weyl duality and its generalizations serve as mathematical tools to understand and establish gauge-string dualities, including AdS/CFT and 2D Yang Mills.

Contribution

It highlights the role of Schur-Weyl duality and related algebraic structures as instrumental in mapping gauge theories to string theories.

Findings

Schur-Weyl duality underpins gauge-string correspondence

Generalizations involve Brauer and Hecke algebras

Applications include AdS/CFT and 2D Yang Mills

Abstract

A class of mathematical dualities have played a central role in mapping states in gauge theory to states in the spacetime string theory dual. This includes the classical Schur-Weyl duality between symmetric groups and Unitary groups, as well as generalisations involving Brauer and Hecke algebras. The physical string dualities involved include examples from the AdS/CFT correspondence as well as the string dual of two-dimensional Yang Mills.