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

The problem of finding a holographic dual to string theory on AdS(3) x S-3 x S-3 x 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) x S-3 x K3 and AdS(3) x S-3 x T-4, there are important qualitative differences. Using an analogue of the elliptic genus for large 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.