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Abstract
Measuring chaos of QCD-like theories is a challenge for formulating a novel characterization of quantum gauge theories. We define a chaos phase diagram of QCD allowing us to locate chaos in the parameter space of energy of homogeneous meson condensates and the QCD parameters such as pion/quark mass. We draw the chaos phase diagrams obtained in two ways: first, by using a linear sigma model, varying parameters of the potential, and second, by using the D4/D6 holographic QCD, varying the number of colors $N_c$ and the 't Hooft coupling constant $\lambda$. A scaling law drastically simplifies our analyses, and we discovered that the chaos originates in the maximum of the potential, and larger $N_c$ or larger $\lambda$ diminishes the chaos.
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