Migdal’s model and Holography

More than 30 years ago Migdal proposed a model for hadronic resonances based on rational approximants [1]. The final aim was to determine the spectrum of vector mesons in the large-Nc limit which best fulfills quarkhadron duality. The strategy was to start from the short distance behavior of the vector vacuum polarization function < V V > and build the Padé approximant thereof. Migdal further suggested to modify the continuum limit to better ensure quark-hadron duality. The final result was a spectrum of single poles located at zeroes of the Bessel J0 function. Migdal’s model of resonances was recently revived [2] in the context of the AdS-QCD holographic models. The so called hard wall model [3] was shown to be the holographic dual of Migdal’s model. Interestingly, another holographic model, the so called soft wall model [4], was recently identified as the holographic dual of the large-Nc Regge model of Ref. [5]. We will reassess Migdal’s model with the help of both the 4-dimensional large-Nc Regge model and the holographic duals. We will see that quarkhadron duality breakdown plays a prominent role and look for its geometrical interpretation in holographic models. We will conclude that the modeling of duality breakdown in Migdal’s model is not compatible with generic features of large-Nc QCD.