Hidden symmetry of correlation functions and amplitudes in N=4 SYM Speaker(s): Gregory Korchemsky
Abstract: We study the fourpoint correlation function of stresstensor supermultiplets in N=4 SYM using the method of Lagrangian insertions. We argue that, as a corollary of N=4 superconformal symmetry, the resulting allloop integrand possesses an unexpected complete symmetry under the exchange of the four external and all the internal (integration) points. This alone allows us to predict the integrand of the threeloop correlation function up to four undetermined constants. Further, exploiting the conjectured amplitude/correlation function duality, we are able to fully determine the threeloop integrand in the planar limit. We perform an independent check of this result by verifying that it is consistent with the operator product expansion, in particular that it correctly reproduces the threeloop anomalous dimension of the Konishi operator. As a byproduct of our study, we also obtain the threepoint function of two halfBPS operators and one Konishi operator at threeloop level. We use the same technique to work out a compact form for the fourloop fourpoint integrand and discuss the generalisation to higher loops.
Date: 18/08/2011  9:30 am
Collection: Integrability in Gauge/String Theories
