Abstract
The problem of finding a holographic dual to string theory on $AdS_3 \times \mathbf{S}^3 \times \mathbf{S}^3 \times \mathbf{S}^1$ is examined in depth. This background supports a large $\mathcal{N}=4$ superconformal symmetry. While in some respects similar to the familiar small $\mathcal{N}=4$ systems on $AdS_3\times \mathbf{S}^3\times K3$ and $AdS_3\times \mathbf{S}^3\times T^4$, there are important qualitative differences. Using an analogue of the elliptic genus for large $\mathcal{N}=4$ 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.
Citation
Sergei Gukov. Emil Martinec. Gregory Moore. Andrew Strominger. "Search for a holographic dual to $AdS_3\times S^3\times S^3\times S^1$." Adv. Theor. Math. Phys. 9 (3) 435 - 525, June 2005.
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