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We provide a concise description of our recent work on the exact conformalfield theory (CFT) formulation of the superstring in the pp-wave backgroundwith Ramond-Ramond (RR) flux, using the Green-Schwarz formalism in thesemi-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 inherentlycoupled and this makes the canonical analysis intractable even at the classicallevel. To overcome this difficulty, we develop a phase-space formulation whichdoes not make use of the equations of motion, and construct two independentsets of Virasoro generators classically. Upon quantization, due to the presenceof the RR flux, the Virasoro algebra generically develops quantum operatoranomalies and only with a judicious choice of normal ordering rescription theycancel between the bosonic and the fermionic contributions. With such properlydefined quantum Virasoro generators, one can construct the BRST operators anddemonstrate that the BRST cohomology analysis reproduces the physical spectrumpreviously obtained in the light-cone gauge.

Superstring in the pp-wave background with RR flux as a conformal field theory