N=(0,4) Quiver $SCFT_2$ and Supergravity on $AdS_3 \times S^2$

We study the proposed duality between the 5-dimensional supergravity/superstring on $AdS_3\times S^2$ and the 2-dimensional N=(0,4) SCFT defined on the boundary of AdS-space. We construct explicitly the N=(0,4) SCFT by imposing the `quiver projection' developed by Douglas-Moore on the N=(4,4) SCFT of symmetric orbifold, which is proposed to be the dual of the 6-dimensional supergravity/superstring on $AdS_3\times S^3$. We explore in detail the spectrum of chiral primaries in this `quiver $SCFT_2$'. We compare it with the Kaluza-Klein spectrum on $AdS_3\times S^2$ and check the consistency between them. We further emphasize that orbifolding of bulk theory should {\em not} correspond to orbifolding of the boundary CFT in the usual sense of two dimensional CFT, rather corresponds to the quiver projection. We observe that these are not actually equivalent with each other when we focus on the multi-particle states.