Out-of-time-order correlators of Skyrmion as baryon in holographic QCD

TL;DR

This paper investigates the out-of-time-order correlator (OTOC) of holographic Skyrmions in QCD, analyzing quantum chaos behavior through numerical and classical approaches within a holographic framework.

Contribution

It provides an analytical and numerical study of the OTOC for holographic Skyrmions derived from the D4/D8 model, including general cases with central force fields.

Findings

OTOC behavior shows large N_c effects but no exponential growth

Classical limit analysis reveals characteristic behaviors of OTOC

Extension to Coulomb potential supports general properties of quantum OTOC

Abstract

As the out-of-time-order correlator (OTOC) is a measure of quantum chaos and an important observable in the context of AdS/CFT, we investigate the OTOC of holographic Skyrmion which is described by an analytical quantum mechanical system from the D4/D8 model (as the holographic QCD). By employing the OTOC defined in quantum mechanics, we derive the formulas and demonstrate the numerical calculations of the OTOC explicitly which is also available for the general case with central force field. Our numerical evaluation illustrates the behaviors of the OTOC with large $N_{c}$, however the expected exponential growth of OTOC is not obtained. Besides, we also take a look at the classical limit of the OTOC and analyze the associated behaviors. At the end of this work, we additionally study the OTOC with three-dimensional Coulomb potential, as another example for the central force field, to support our analyses of the general properties of quantum OTOC.