#### Marco Bochicchio (INFN, Roma)

## Renormalization in large-N QCD is incompatible with Open/Closed String Duality

Abstract

We demonstrate that Renormalization Group and Asymptotic Freedom imply that the large-N ’t Hooft expansion of the S-matrix in YM is ultraviolet finite, while it is renormalizable but not ultraviolet finite in QCD with massless quarks, due to log divergences of meson loops starting at order of N_f/N. We investigate the compatibility of these renormalization properties with the Open/Closed Duality of a would-be String Solution, by means of a new version in large-N massless QCD of a SVZ low-energy theorem.
It turns out that the large-N QCD low-energy theorem is incompatible with Open/Closed Duality.
The same conclusion is reached if it is assumed, as it is universally believed, that large-N massless QCD has a mass gap in the glueball sector. Similar considerations apply to QCD with massive quarks, and to a vast class of confining massive QCD-like theories, provided a renormalization scheme exists, as MS, in which the beta function is independent on the masses.