Giant Graviton Oscillators

TL;DR

This paper investigates the action of the dilatation operator on specific restricted Schur polynomials in N=4 super Yang-Mills theory, revealing potential non-planar integrability through a harmonic oscillator analogy.

Contribution

It introduces a new Schur-Weyl duality approach to evaluate the dilatation operator on complex Young diagram-labeled polynomials, extending integrability insights beyond the planar limit.

Findings

Dilatation operator reduces to harmonic oscillators

Evidence for non-planar integrability in large N limit

Connection to Gauss Law constraints for branes

Abstract

We study the action of the dilatation operator on restricted Schur polynomials labeled by Young diagrams with p long columns or p long rows. A new version of Schur-Weyl duality provides a powerful approach to the computation and manipulation of the symmetric group operators appearing in the restricted Schur polynomials. Using this new technology, we are able to evaluate the action of the one loop dilatation operator. The result has a direct and natural connection to the Gauss Law constraint for branes with a compact world volume. We find considerable evidence that the dilatation operator reduces to a decoupled set of harmonic oscillators. This strongly suggests that integrability in N=4 super Yang-Mills theory is not just a feature of the planar limit, but extends to other large N but non-planar limits.