Emergent Threebrane Lattices

TL;DR

This paper investigates the anomalous dimensions of specific operators in Yang Mills theory, revealing a lattice structure emerging from Young diagrams that describe excited states of giant gravitons.

Contribution

It introduces a novel lattice interpretation of the dilatation operator for operators dual to giant graviton states using Young diagrams.

Findings

The dilatation operator acts like a second derivative on a lattice.

Young diagrams with two columns encode the lattice structure.

The study connects operator dimensions to emergent lattice geometries.

Abstract

In this article the anomalous dimension of a class of operators with a bare dimension of O(N) is studied. The operators considered are dual to excited states of a two giant graviton system. In the Yang Mills theory they are described by restricted Schur polynomials, labeled with Young diagrams that have at most two columns. In a certain limit the dilatation operator looks like a lattice version of a second derivative, with the lattice emerging from the Young diagram itself.