  We study solutions of the one-loop beta-functions of the critical bosonic
string theory in the framework of the Renormalization Group (RG) approach to
string theory, considering explicitly the effects of the 21 extra dimensions.
In the RG approach the 26-dimensional manifold is given in terms of a four
dimensional Minkowski spacetime times R and a 21-dimensional hyper-plane. In
calculating the Wilson loops, as it is wellknown for this kind of confining
geometry, two phenomena appear: confinement and over-confinement. There is a
critical minimal surface below of which it leads to confinement only. The role
of the extra dimensions is understood in terms of a dimensionless scale l
provided by them. Therefore the effective string tension in the area law, the
length of the Wilson loops, as well as, the size of the critical minimal
surface depend on this scale. When this confining geometry is used to study a
field-theory beta-function with an infrared attractive point (as the
Novikov-Shifman-Vainshtein-Zakharov beta-function) the range of the couplings
where the field theory is confining depends on that scale. We have explicitly
calculated the l-dependence of that range.
