Worldsheet properties of extremal correlators in AdS/CFT

Abstract

We continue to investigate planar four point worldsheet correlators of string theories which are conjectured to be duals of free gauge theories. We focus on the extremal correlators langTr(ZJ1(x))Tr(ZJ2(y))Tr(ZJ3(z))Tr(bar ZJ(0)))rang of Script N = 4 SYM theory, and construct the corresponding worldsheet correlators in the limit when the Ji >> 1. The worldsheet correlator gets contributions, in this limit, from a whole family of Feynman graphs. We find that it is supported on acurve in the moduli space parametrized by the worldsheet crossratio. In a further limit of the spacetime correlators we find this curve to be the unit circle. In this case, we also check that the entire worldsheet correlator displays the appropriate crossing symmetry. The non-renormalization of the extremal correlators in the 't Hooft coupling offers a potential window for a comparison of these results with those from strong coupling.