Non-planar corrections in the symmetric orbifold
Matthias R. Gaberdiel, Beat Nairz, Cheng Peng
TLDR
This paper calculates non-planar corrections in the symmetric orbifold, revealing lifted degeneracies, quantum chaos, and integrability only in the planar limit.
Key contributions
- Calculates non-planar corrections to anomalous dimensions of quarter BPS states.
- Shows these corrections lift spectral degeneracies for large twist and N.
- Reveals signatures of quantum chaos, including level repulsion.
- Suggests integrability in symmetric orbifold is limited to the planar (large N) limit.
Why it matters
This paper is significant as it challenges the assumption of integrability in the symmetric orbifold beyond the planar limit. By revealing quantum chaos signatures, it provides new insights into the fundamental nature of these systems, relevant for string theory and black hole physics.
Original 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.
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