Search for a holographic dual to AdS₃× S³× S³× S¹

The problem of finding a holographic dual to string theory on AdS 3 S 3 S 3 S 1 is examined in depth. This background supports a large N = 4 superconformal symmetry. While in some respects similar to the familiar small N = 4 systems on AdS 3 S 3 K3 and AdS 3 S 3 T 4 , there are important qualitative differences. Using an analogue of the elliptic genus for large N = 4 theories we rule out all extant proposalsin 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.