  We found a quantum perfect lattice action in the 4-dimensional monopole
current theory which is known as an effective theory in the infrared region of
QCD. The perfect monopole action is transformed exactly into a lattice action
of a string model. When the monopole interactions are weak as in the case of
infrared SU(2) QCD, the string interactions are strong. The static potential
and the string tension in this region can be estimated analytically by the use
of the strong coupling expansion.
