Chaos in the holographic matrix models for meson and baryon

Abstract: In recent years, the investigation of chaos has become a bridge connecting gravity theory and quantum field theory, especially within the framework of gauge-gravity duality. In this work, we study holographically the chaos in the matrix models for meson and baryon, which are derived from the $\mathrm{D4}/\mathrm{D6}/\overline{\mathrm{D6}}$ approach as a top-down holographic model for QCD. Since these matrix models can be simplified into coupled oscillator models with special parameters, we analyze the chaos in the resultant coupled oscillators. In the analysis of the classical chaos, we calculate numerically the orbits on the Poincar\'e section, the Lyapunov exponent as a function of the total energy and derive the large $N_{c}$ behavior analytically, then discuss the possible phase structure both in the mesonic and baryonic matrix models. These analyses suggest that chaos might serve as an order parameter to detect the gauge theory with spontaneous breaking or restoration of symmetry. Besides, in the analysis of the quantum chaos, we demonstrate the numerical calculation of the OTOCs and analytically derive their large $N_{c}$ behavior by using the perturbation method in quantum mechanics. The numerical calculation illustrates there is a critical temperature, as a critical energy scale, that the OTOC begins to saturate, which covers qualitatively the classical analysis of the Lyapunov exponent. And the large $N_{c}$ analytics indicates the OTOCs are suppressed by the growth of $N_{c}$. Overall, the investigation of chaos in this work may be helpful to identify common features shared by the matrix models, hadronic physics, gauge theory, quantum mechanics, and gravity theory.