B-RNS-GSS Type II superstring in Ramond-Ramond backgrounds

The B-RNS-GSS formalism containing both RNS and GS worldsheet variables is extended for the description of the Type II superstring in curved backgrounds. The BRST charge of the theory is expressed in terms of $N=(1,1)$ superconformal generators $(T,G; {\widehat{T}}, {\widehat{G}})$, and the classical anticommutation relations $\{G,G\}=-2T$ and $\{{\widehat{G}},{\widehat{G}}\}=-2{\widehat{T}}$ are shown to imply the Type II supergravity equations of motion. The particular case of the Type IIB superstring in an $AdS_5\times S^5$ background is discussed and shown to be classically integrable.