On the worldsheet theories of strings dual to free largeNgauge theories

We analyze in detail some properties of the worldsheet of the closed stringtheories suggested by Gopakumar to be dual to free large N SU(N) gauge theories(with adjoint matter fields). We use Gopakumar's prescription to translate thecomputation of space-time correlation functions to worldsheet correlationfunctions for several classes of Feynman diagrams, by explicit computations ofStrebel differentials. We compute the worldsheet operator product expansion inseveral cases and find that it is consistent with general worldsheet conformalfield theory expectations. A peculiar property of the construction is that inseveral cases the resulting worldsheet correlation functions are non-vanishingonly on a sub-space of the moduli space (say, for specific relations betweenvertex positions). Another strange property we find is that for a conformallyinvariant space-time theory, the mapping to the worldsheet does not preservethe special conformal symmetries, so that the full conformal group is notrealized as a global symmetry on the worldsheet (even though it is, byconstruction, a symmetry of all integrated correlation functions).Comment: 60 pages, 17 figures, latex. v2: Added references and a minor correctio