  We study the type IIB superstring in the plane-wave background with
Ramond-Ramond flux and formulate it as an exact conformal field theory in
operator formalism. One of the characteristic features of the superstring in a
consistent background with RR flux, such as the AdS5xS5 and its plane-wave
limit, is that the left- and the right-moving degrees of freedom on the
worldsheet are inherently coupled. In the plane-wave case, it is manifested in
the well-known fact that the Green-Schwarz formulation of the theory reduces to
that of free massive bosons and fermions in the light-cone gauge. This raises
the obvious question as to how this feature is reconciled with the underlying
conformal symmetry of the string theory. By adopting the semi-light-cone
conformal gauge, we will show that, despite the existence of such non-linear
left-right couplings, one can construct two independent sets of quantum
Virasoro operators in terms of fields obeying the free-field commutation
relations. Furthermore, we demonstrate that the BRST cohomology analysis
reproduces the physical spectrum obtained in the light-cone gauge.
