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

TL;DR

This work addresses AdS$_3$/CFT$_2$ with reduced supersymmetry by constructing an explicit boundary $N=(0,4)$ SCFT$_2$ through a Douglas–Moore quiver projection from the $N=(4,4)$ symmetric orbifold. The authors define the Hilbert space via a quiver-invariant projection and analyze the chiral primaries across untwisted and twisted sectors, showing a complete match with the Kaluza–Klein spectrum of 5d SUGRA on $AdS_3\times S^2$ in the Maldacena limit. They demonstrate that bulk orbifolding does not correspond to a simple boundary orbifold, but to a boundary quiver projection, which correctly accounts for multi-particle states and the so-called stringy exclusion principle. The results support the viability of a reduced-supersymmetry AdS$_3$/CFT$_2$ duality and clarify how boundary theories emerge from bulk orbifold procedures, while outlining important open issues such as modular invariance and extensions to more general compactifications.

Abstract

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.