From correlation functions to event shapes

International audienceWe present a new approach to computing event shape distributions or, moreprecisely, charge flow correlations in a generic conformal field theory (CFT).These infrared finite observables are familiar from collider physics studiesand describe the angular distribution of global charges in outgoing radiationcreated from the vacuum by some source. The charge flow correlations can beexpressed in terms of Wightman correlation functions in a certain limit. Weexplain how to compute these quantities starting from their Euclidean analoguesby means of a non-trivial analytic continuation which, in the framework of CFT,can elegantly be performed in Mellin space. The relation between the chargeflow correlations and Euclidean correlation functions can be reformulateddirectly in configuration space, bypassing the Mellin representation, as acertain Lorentzian double discontinuity of the correlation function integratedalong the cuts. We illustrate the general formalism in N=4 SYM, making use ofthe well-known results on the four-point correlation function of half-BPSscalar operators. We compute the double scalar flow correlation in N=4 SYM, atweak and strong coupling and show that it agrees with known results obtained bydifferent techniques. One of the remarkable features of the N=4 theory is thatthe scalar and energy flow correlations are proportional to each other.Imposing natural physical conditions on the energy flow correlations(finiteness, positivity and regularity), we formulate additional constraints onthe four-point correlation functions in N=4 SYM that should be valid at anycoupling and away from the planar limit