Non-planar Anomalous Dimensions in the sl(2) Sector

TL;DR

This paper calculates non-planar one-loop anomalous dimensions of restricted Schur polynomials in the sl(2) sector of N=4 super Yang-Mills, revealing a reduction to harmonic oscillators and the emergence of the Gauss Law for giant gravitons.

Contribution

It demonstrates that the non-planar dilatation operator in the sl(2) sector simplifies to decoupled harmonic oscillators, extending understanding of gauge/string duality.

Findings

Dilatation operator reduces to harmonic oscillators

Emergence of Gauss Law for giant gravitons

Diagonalization parallels the su(2) sector

Abstract

In this note we compute the non-planar one loop anomalous dimension of restricted Schur polynomials that belong to the sl(2) sector of N=4 super Yang-Mills theory and have a bare dimension of order N. Although the details are rather different, ultimately the problem of diagonalizing the dilatation operator in the sl(2) sector can be reduced to the su(2) sector problem. In this way we establish the expected dynamical emergence of the Gauss Law for giant gravitons and further show that the dilatation operator reduces to a set of decoupled harmonic oscillators.