Differential equations for on-shell loop integrals

by Johannes Henn

Tuesday 7 Dec 2010, 14:00 → 15:00 Europe/Zurich

TH Theory Conference Room (CERN)

In this talk I review recent developments in the understanding of planar loop amplitudes in N=4 super Yang Mills. The latter have a dual conformal symmetry which can be made manifest at loop level by using a Higgs mechanism to regulate infrared divergences. Very recently, it was shown that the n-point two-loop MHV amplitudes can be written in terms a small set of dual conformal integrals with certain numerator factors. I show that precisely those integrals satisfy second-order differential equations. The differential equations have an iterative structure and reduce the loop order by one. A consequence of the differential equations is that the integrals we discuss are not arbitrarily complicated transcendental functions. I present full analytic results for a five- and seven-point integral in terms of harmonic polylogarithms. Finally, I comment on generalizations to other theories and make comments on the basis of loop integrals.