  The renormalization group equations of the Yang-Mills theory are examined in
the non-critical string theory according to the framework of the holography.
Under a simple ansatz for the tachyon, we could find several interesting
solutions which are classified by the value of the tachyon potential at the
vacuum. We show two typical, asymptotic-free solutions which are different in
their infrared behaviors. For both types of solutions, we could obtain
quark-confinement potential from the Wilson-loop. The stability of the tachyon
and the ZigZag symmetry are also discussed for these solutions.
