Search for a holographic dual to $\textit{AdS}_3\times S^3\times S^3\times S^1$

The problem of finding a holographic dual to string theory on $AdS_3 \times \S^3 \times \S^3 \times \S^1$ is examined in depth. This background supports a large $\CN=4$ superconformal symmetry. While in some respects similar to the familiar small $\CN=4$ systems on $AdS_3\times \S^3\times K3$ and $AdS_3\times \S^3\times T^4$, there are important qualitative differences. Using an analogue of the elliptic genus for large $\CN=4$ theories we rule out all extant proposals--in their simplest form--for a holographic duality to supergravity at generic values of the background fluxes. Modifications of these extant proposals and other possible duals are discussed.

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Published 1 January 2005