Semiclassical SL(2) strings on LLM backgrounds

We study semi-classical string solutions that live on white regions of the LLM plane for a generic LLM geometry. These string excitations are labelled by conserved charges E,J and S and are thus holographically dual to operators in the SL(2) sector of N=4 super Yang-Mills made up of covariant derivatives acting on complex scalar fields Z. On the other hand, the LLM geometry itself is dual to an operator consisting of O(N2)Z-fields so that the operators dual to our solutions, containing both the stringy excitation and background, are non-planar. In an appropriate short string limit we argue that the string solution we find should be dual to a localised SL(2) operator in the gauge theory language. This allows us to perform a non-trivial check of the recent proposal that the dynamics of localised operators should be identical, up to a rescaling of the 't Hooft coupling, to the dynamics of those same excitations in the AdS5×S5 background.