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

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