From correlation functions to event shapes

TL;DR

This paper introduces a novel method for calculating event shape distributions in conformal field theories, linking Euclidean and Lorentzian correlators via Mellin space and analytic continuation, with applications to N=4 SYM.

Contribution

It develops a new formalism for computing charge flow correlations from Euclidean correlators using Mellin space and Lorentzian discontinuities, demonstrated in N=4 SYM at various couplings.

Findings

Computed double scalar flow correlation in N=4 SYM at weak and strong coupling.

Established proportionality between scalar and energy flow correlations in N=4 SYM.

Derived constraints on four-point functions from physical conditions on flow correlations.

Abstract

We present a new approach to computing event shape distributions or, more precisely, charge flow correlations in a generic conformal field theory (CFT). These infrared finite observables are familiar from collider physics studies and describe the angular distribution of global charges in outgoing radiation created from the vacuum by some source. The charge flow correlations can be expressed in terms of Wightman correlation functions in a certain limit. We explain how to compute these quantities starting from their Euclidean analogues by means of a non-trivial analytic continuation which, in the framework of CFT, can elegantly be performed in Mellin space. The relation between the charge flow correlations and Euclidean correlation functions can be reformulated directly in configuration space, bypassing the Mellin representation, as a certain Lorentzian double discontinuity of the correlation function integrated along the cuts. We illustrate the general formalism in N=4 SYM, making use of the well-known results on the four-point correlation function of half-BPS scalar operators. We compute the double scalar flow correlation in N=4 SYM, at weak and strong coupling and show that it agrees with known results obtained by different techniques. One of the remarkable features of the N=4 theory is that the 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 on the four-point correlation functions in N=4 SYM that should be valid at any coupling and away from the planar limit.