Scrambling without chaos in RCFT
Pawel Caputa, Tokiro Numasawa, Alvaro Veliz-Osorio
TL;DR
The paper addresses chaos and entanglement in $1+1$-dimensional RCFTs by deriving a universal late-time OTOC value governed by the anyon monodromy scalar $\frac{S^*_{ij}}{S_{00}}$ up to the appropriate quantum-dimension normalization. It contrasts this with purity, which at late times yields $\log d_{\mathcal{O}}$, reflecting non-perturbative data of the conformal family, and shows that in the large-$c$ limit purity can grow logarithmically with time as in holography while OTOCs remain non-chaotic (non-vanishing constants). The authors test these ideas in the integrable $SU(N)_k$ WZW model, demonstrating exact matching between late-time OTOCs and the modular S-matrix and revealing level-rank duality in the quantum dimensions. In the large-$c$ 't Hooft limit, the two measures separate: purity exhibits scrambling with $\Delta S_A^{(2)}(t) \sim 2h\log(2t/\epsilon)$, whereas OTOCs stay finite, underscoring that scrambling of entanglement does not imply chaotic dynamics. This work clarifies how non-perturbative data survive scrambling and suggests experimental routes to access modular data via OTOCs in RCFTs.
Abstract
In this paper we investigate measures of chaos and entanglement in rational conformal field theories in 1+1 dimensions. First, we derive a universal formula for the late time value of the out-of-time-ordered correlators for this class of theories. Our universal result can be expressed as a particular combination of the modular S-matrix elements known as the anyon monodromy scalar. Next, in the explicit setup of a $SU(N)_k$ Wess-Zumino-Witten model, we compare the late time behavior of the out-of-time-ordered correlators and the purity. Interestingly, in the large-c limit, the purity grows logarithmically as in holographic theories; in contrast, the out-of-time-ordered correlators remain, in general, non-vanishing.