From Large N Nonplanar Anomalous Dimensions to Open Spring Theory

TL;DR

This paper computes non-planar one-loop anomalous dimensions of certain operators in gauge theory, mapping the problem to a classical spring model, revealing insights into the spectrum of these operators.

Contribution

It introduces a method to diagonalize the dilatation operator for restricted Schur polynomials using U(N) representation theory, connecting to a classical spring model.

Findings

Spectrum matches a classical spring model

Method simplifies non-planar anomalous dimension calculations

Provides a new perspective on operator spectra in gauge theories

Abstract

In this note we compute the non-planar one loop anomalous dimension of restricted Schur polynomials that have a bare dimension of O(N). This is achieved by mapping the restricted Schur polynomials into states of a specific U(N) irreducible representation. In this way the dilatation operator is mapped into a u(n) valued operator and, as a result, can easily be diagonalized. The resulting spectrum is reproduced by a classical model of springs between masses.