We study the out-of-time-order correlators (OTOC) of Skyrmion as baryon in the D0-D4/D8 model which is expected to be holographically dual to QCD with instantons as D0-branes or with a non-zero theta angle. Baryon states are identified to the excitations of the Skyrmion which are described by a holographic quantum mechanical system in this model. By employing the definition of OTOC in quantum mechanics, we derive the formulas and demonstrate explicitly the numerical calculations of the OTOC. Our calculation illustrates the quantum OTOC with imaginary Lyapunov coefficient indicates the possibly metastable baryonic status in the presence of the instanton while the classical OTOC can not, thus it reveals the instantonic or theta-dependent features of QCD are dominated basically by its quantum properties. Furthermore, the OTOC also implies the baryonic phase becomes really chaotic with real Lyapunov exponent if the instanton charge increases sufficiently which agrees with the unstable baryon spectrum presented in this model. In this sense, we believe the OTOC may be treated as a tool to detect the baryonic phase structure of QCD.

中文翻译：

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乱序相关器作为瞬子全息 QCD 重子相结构探测器


我们研究了 D0-D4/D8 模型中作为重子的斯格明子的乱序相关器 (OTOC)，预计该模型将与 QCD 全息对偶，瞬时子作为 D0 膜或具有非零 θ 角。重子态被识别为斯格明子的激发，该激发由该模型中的全息量子力学系统描述。通过采用量子力学中OTOC的定义，我们推导了公式并明确地证明了OTOC的数值计算。我们的计算表明，具有虚数李亚普诺夫系数的量子OTOC表明在瞬子存在的情况下可能存在亚稳态重子状态，而经典OTOC则不能，因此它揭示了QCD的瞬时或θ相关特征基本上由其量子特性决定。此外，OTOC 还意味着，如果瞬时电荷充分增加，重子相将变得非常混乱，且具有真实的 Lyapunov 指数，这与该模型中呈现的不稳定重子谱一致。从这个意义上说，我们认为OTOC可以作为检测QCD重子相结构的工具。