  We find an interesting connection between perturbative large N gauge theory
and closed superstrings. The gauge theory in question is found on N D3-branes
placed at the tip of the cone R^6/Gamma. In our previous work we showed that,
when the orbifold group Gamma breaks all supersymmetry, then typically the
gauge theory is not conformal because of double-trace couplings whose one-loop
beta functions do not possess real zeros. In this paper we observe a precise
correspondence between the instabilities caused by the flow of these
double-trace couplings and the presence of tachyons in the twisted sectors of
type IIB theory on orbifolds R^{3,1}x R^6/Gamma. For each twisted sectors that
does not contain tachyons, we show that the corresponding double-trace coupling
flows to a fixed point and does not cause an instability. However, whenever a
twisted sector is tachyonic, we find that the corresponding one-loop beta
function does not have a real zero, hence an instability is likely to exist in
the gauge theory. We demonstrate explicitly the one-to-one correspondence
between the regions of stability/instability in the space of charges under
Gamma that arise in the perturbative gauge theory and in the free string
theory. Possible implications of this remarkably simple gauge/string
correspondence are discussed.
