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

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