Worldsheet Properties of Extremal Correlators in AdS/CFT

TL;DR

This paper investigates extremal four-point correlators in N=4 SYM theory within the AdS/CFT framework, revealing their worldsheet support on a curve in moduli space and confirming crossing symmetry, with implications for non-renormalization properties.

Contribution

It constructs the worldsheet correlators for extremal four-point functions at large charges and shows their support on a moduli space curve, advancing understanding of dual string theory correlators.

Findings

Worldsheet correlators supported on a curve in moduli space.

Curve reduces to the unit circle in a specific limit.

Correlators exhibit crossing symmetry and non-renormalization.

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 <Tr(Z^{J_1}(x)) Tr(Z^{J_2}(y)) Tr(Z^{J_3}(z)) Tr(\bar{Z}^{J}(0))> of $N = 4$ SYM theory, and construct the corresponding worldsheet correlators in the limit when the $J_i >> 1$. The worldsheet correlator gets contributions, in this limit, from a whole family of Feynman graphs. We find that it is supported on a {\it curve} in the moduli space parametrised 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.