  We provide a concise description of our recent work on the exact conformal
field theory (CFT) formulation of the superstring in the pp-wave background
with Ramond-Ramond (RR) flux, using the Green-Schwarz formalism in the
semi-light-cone conformal gauge. Due to the presence of the RR flux, the left-
and the right-moving degrees of freedom on the worldsheet are inherently
coupled and this makes the canonical analysis intractable even at the classical
level. To overcome this difficulty, we develop a phase-space formulation which
does not make use of the equations of motion, and construct two independent
sets of Virasoro generators classically. Upon quantization, due to the presence
of the RR flux, the Virasoro algebra generically develops quantum operator
anomalies and only with a judicious choice of normal ordering rescription they
cancel between the bosonic and the fermionic contributions. With such properly
defined quantum Virasoro generators, one can construct the BRST operators and
demonstrate that the BRST cohomology analysis reproduces the physical spectrum
previously obtained in the light-cone gauge.
