  We study large-N double-scaling limits of U(N) gauge theories in four
dimensions. We focus on theories in a partially confining phase where an
abelian subgroup $\hat{G}$ of the gauge group remains unconfined.
Double-scaling is defined near critical points in the parameter/moduli space
where states charged under $\hat{G}$ become massless. In specific cases, we
present evidence that the double-scaled theory is dual to a non-critical
superstring background. Models studied include the $\beta$-deformation of
${\cal N}=4$ SUSY Yang-Mills which leads to a non-critical string theory with
sixteen supercharges. We also study ${\cal N}=1$ SUSY Yang-Mills theory coupled
to a single chiral superfield with a polynomial superpotential which leads to a
related string theory with eight supercharges. In both cases the string
coupling is small and the background is free from Ramond-Ramond flux.
