Hints of Integrability Beyond the Planar Limit: Nontrivial Backgrounds

TL;DR

This paper investigates whether integrability persists in certain quantum field theory models beyond the planar limit by analyzing non-planar corrections related to heavy operators, finding potential cases where integrability remains.

Contribution

It introduces a limit where non-planar corrections from backreaction do not destroy integrability, suggesting possible integrability beyond the planar approximation.

Findings

Non-planar corrections can be summed to include backreaction effects.

A specific limit exists where integrability might be preserved.

Conserved charges indicate potential integrability beyond the planar limit.

Abstract

The problem of computing the anomalous dimensions of a class of (nearly) half-BPS operators with a large R-charge is reduced to the problem of diagonalizing a Cuntz oscillator chain. Due to the large dimension of the operators we consider, non-planar corrections must be summed to correctly construct the Cuntz oscillator dynamics. These non-planar corrections do not represent quantum corrections in the dual gravitational theory, but rather, they account for the backreaction from the heavy operator whose dimension we study. Non-planar corrections accounting for quantum corrections seem to spoil integrability, in general. It is interesting to ask if non-planar corrections that account for the backreaction also spoil integrability. We find a limit in which our Cuntz chain continues to admit extra conserved charges suggesting that integrability might survive.