Non-planar corrections in the symmetric orbifold

TL;DR

This paper computes non-planar corrections to BPS states in a symmetric orbifold, revealing degeneracy lifting and signs of quantum chaos, indicating integrability is limited to the large N limit.

Contribution

It introduces calculations of non-planar corrections in symmetric orbifolds, showing degeneracy lifting and chaos signatures beyond the planar approximation.

Findings

Degeneracies are lifted by non-planar corrections.

Signatures of quantum chaos are observed.

Integrability appears only in the large N limit.

Abstract

We calculate the non-planar corrections to the anomalous dimensions of certain quarter BPS states in the symmetric product orbifold $\text{Sym}^N \big({\mathbb{T}^4}\big)$. We find that some of the degeneracies in the spectrum for large twist $w$ and large $N$ are lifted by these contributions. We furthermore find signatures of quantum chaos, namely level repulsion and random matrix statistics. This suggests that integrability is only present in the symmetric orbifold in the planar (i.e. large $N$) limit.