  The solution of the large-N 't Hooft limit of QCD is universally believed to
be a String Theory of Closed Strings in the Glueball Sector and of Open Strings
in the Meson Sector. Yet, we prove a no-go theorem, that the large-N limit of
QCD with massless quarks, or more generally, that the large-N limit of a vast
class of confining, i.e. with a Mass Gap in the Glueball Sector,
asymptotically-free Gauge Theories coupled to matter fields with no mass scale
in perturbation theory cannot be a canonically-defined String Theory of Closed
and Open Strings, i.e. admitting Open/Closed Duality. The no-go theorem occurs
because Open/Closed Duality, implying that the ultraviolet divergences of
annulus diagrams in the Open Sector arise from infrared divergences of tadpoles
of massless particles in the Closed Sector, turns out to be incompatible with
the existence of the Mass Gap in the Glueball Sector of confining
asymptotically-free theories with no mass scale in perturbation theory in
which, as for example in QCD, the first coefficient of the beta function for 't
Hooft gauge coupling gets $1/N$ corrections due to the matter fields. Moreover,
we suggest a way-out to the no-go theorem on the basis of a new non-canonical
construction of the String S-matrix for asymptotically-free Gauge Theories such
as large-N QCD, involving Topological Strings on Non-Commutative Twistor Space.
