  The correspondence of the non-critical string theory and the Yang-Mills
theory is examined according to the recent Polyakov's proposal, and two
possible solutions of the bulk equations are addressed near the fixed points of
the pure Yang-Mills theory: (i) One solution asymptotically approaches to the
AdS space at the ultraviolet limit where the conformally invariant field theory
is realized. (ii) The second one approaches to the flat space in both the
infrared and the ultraviolet limits. The area law of the Wilson-loop and the
asymptotic freedom with logarithmic behaviour are seen in the respective limit.
