Young diagrams, Brauer algebras, and bubbling geometries

TL;DR

This paper explores the relationship between 1/4 BPS geometries in string theory and algebraic structures like Young diagrams and Brauer algebras, revealing how geometric configurations encode algebraic operator classifications.

Contribution

It establishes a novel mapping between droplet geometries and Young diagrams of the Brauer algebra, linking geometric features to algebraic operator classifications in ${ m f N}=4$ SYM.

Findings

Mapped droplet configurations to Young diagrams of the Brauer algebra.

Linked the integer $k$ to angular direction mixing in geometries.

Provided insights into the geometric interpretation of algebraic operator labels.

Abstract

We study the 1/4 BPS geometries corresponding to the 1/4 BPS operators of the dual gauge theory side, in ${\cal N}=4$ SYM. By analyzing asymptotic structure and flux integration of the geometries, we present a mapping between droplet configurations arising from the geometries and Young diagrams of the Brauer algebra. In particular, the integer $k$ classifying the operators in the Brauer basis is mapped to the mixing between the two angular directions.