Renormalization in large-N QCD is incompatible with open/closed string duality

Publication date: Available online 11 July 2018Source: Physics Letters BAuthor(s): M. BochicchioAbstractSolving by a canonical string theory, of closed strings for the glueballs and open strings for the mesons, the 't Hooft large-N expansion of QCD is a long-standing problem that resisted all the attempts despite the advent of the celebrated gauge/gravity duality in the framework of string theory. We demonstrate that in the canonical string framework such a solution does not actually exist because an inconsistency arises between the renormalization properties of the QCD S matrix at large-N, recently worked out in Bochicchio (2017) [5], and the open/closed duality of the would-be string solution. Specifically, the would-be open-string one-loop corrections to the tree glueball amplitudes must be ultraviolet (UV) divergent by the aforementioned renormalization properties, which follow from the QCD asymptotic freedom (AF) and renormalization group. Hence, naively, the inconsistency arises because these amplitudes are dual to tree closed-string diagrams, which are universally believed to be both UV finite – since they are closed-string tree diagrams – and infrared (IR) finite because of the glueball mass gap. In fact, the inconsistency follows from a low-energy theorem of the Novikov–Shifman–Vainshtein–Zakharov (NSVZ) type derived in Bochicchio (2017) [5] that controls the renormalization in QCD-like theories. The aforementioned inconsistency extends to the would-be cano...

Source: Physics Letters B - July 11, 2018 Category: Physics Source Type: research