Nonplanar integrability at two loops

TL;DR

This paper demonstrates that the su(2) sector of a gauge theory remains integrable at two loops in a non-planar large N limit, with the spectrum related to decoupled harmonic oscillators.

Contribution

It shows that operators diagonalizing the one-loop dilatation operator are not corrected at two loops in the displaced corners approximation, revealing non-planar integrability.

Findings

Operators are not corrected at two loops in the large N limit.

Spectrum of anomalous dimensions relates to decoupled harmonic oscillators.

Spectrum is continuous at large N and discrete at finite N.

Abstract

In this article we compute the action of the two loop dilatation operator on restricted Schur polynomials that belong to the su(2) sector, in the displaced corners approximation. In this non-planar large N limit, operators that diagonalize the one loop dilatation operator are not corrected at two loops. The resulting spectrum of anomalous dimensions is related to a set of decoupled harmonic oscillators, indicating integrability in this sector of the theory at two loops. The anomalous dimensions are a non-trivial function of the 't Hooft coupling, with a spectrum that is continuous and starting at zero at large N, but discrete at finite N.