Complex 2D Matrix Model and Geometrical Map on Complex-Nc Plane

We study the parameter dependence of the internal structure of resonance states by formulating Complex two-dimensional (2D) Matrix Model, where the two dimensions represent two-levels of resonances. We calculate a critical value of the parameter at which "nature transition" with character exchange occurs between two resonance states, from the viewpoint of geometry on complex-parameter space. Such critical value is useful to know the internal structure of resonance states with variation of the parameter in the system. We apply the model to analyze the internal structure of hadrons with variation of the color number Nc from infinity to a realistic value 3. By regarding 1/Nc as the variable parameter in our model, we calculate a critical color number of nature transition between hadronic states in terms of quark-antiquark pair and mesonic molecule as exotics from the geometry on complex-Nc plane. For the large-Nc effective theory, we employ the chiral Lagrangian induced by holographic QCD with D4/D8/D8-bar multi-D brane system in the type IIA superstring theory.