Conformal symmetry of superstrings on $Ad{S}_3\times S^3\times T^4$ and D1/D5 system

Conformal field theory of the D1/D5 system and superstrings on $AdS_3\times S^3\times T^4$ is studied with particular attention to the world-sheet fields corresponding to the $T^4$ part. A solution to the spacetime N=4 superconformal symmetry doubling and other problems is proposed. It is argued that the relevant spacetime symmetry should be based on the middle N=4 superconformal algebra. It is discussed as to why this superconformal structure has been missed so far.