Marco Bochicchio (Roma): Renormalization in large‐N QCD and open/closed string duality

We demonstrate that the asymptotic freedom and renormalization group imply that the large‐N ’t Hooft expansion of the YM S matrix is ultraviolet (UV) finite nonperturbatively, while the large‐N expansion of the QCD S matrix is only renormalizable, due to UV divergences starting from the order of N_f/N, with N_f the number of quark flavors. We investigate the compatibility of the aforementioned renormalization properties with the existence of a supposed canonical string solution, matching the topology of ’t Hooft
large‐N expansion, for the S matrix of large‐N YM theory and QCD. The UV finiteness of the large‐N YM S matrix is compatible with the universally believed UV finiteness of closed string theories. Yet, we demonstrate that the aforementioned renormalization properties of the large‐N QCD S matrix to the order of N_f/N are incompatible with the open/closed string duality of the would‐be canonical string solution, which therefore does not exist. We suggest a noncanonical way‐out based on topological string on
noncommutative twistor space.