  Solving 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 $N$ -- a consequence of the asymptotic
freedom (AF) -- 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. 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 finite because of the glueball mass
gap. In fact, the inconsistency follows from a low-energy theorem of the NSVZ
type that controls the renormalization in QCD-like theories. The inconsistency
extends to the would-be canonical string for a vast class of 't Hooft large-$N$
QCD-like theories including $\mathcal{N}=1$ SUSY QCD. We also demonstrate that
the presently existing SUSY string models with a mass gap -- such as
Klebanov-Strassler, Polchinski-Strassler (PS) and certain PS variants -- cannot
contradict the above-mentioned results since they are not asymptotically free.
Moreover, we shed light on the way the open/closed string duality may be
perturbatively realized in these string models compatibly with a mass gap in
the 't Hooft-planar closed-string sector and the low-energy theorem because of
the lack of AF. Finally, we suggest a noncanonical way-out for QCD-like
theories based on topological strings on noncommutative twistor space.
