TY - JOUR

T1 - From correlation functions to event shapes

AU - Belitsky, Andrei

AU - Hohenegger, S.

AU - Korchemsky, G. P.

AU - Sokatchev, E.

AU - Zhiboedov, A.

N1 - Funding Information:
We would like to thank Vladimir Braun, Simon Caron-Huot, Juan Maldacena and Raymond Stora for interesting discussions. We are indebted to Juan Maldacena for careful reading of the manuscript and useful comments. The work of A.B. was supported by the U.S. National Science Foundation under the grant No. PHY-1068286 and CNRS . G.K. and E.S. acknowledge partial support by the French National Agency for Research ( ANR ) under contract StrongInt ( BLANC-SIMI-4-2011 ). A.Z. was supported in part by the U.S. National Science Foundation under Grant No. PHY-0756966 . A.B., S.H. and A.Z. are grateful to the Institut de Physique Théorique (Saclay) for the hospitality extended to them at various stages of the project.

PY - 2014/7

Y1 - 2014/7

N2 - 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 nontrivial analytic continuation which, in the framework of CFT, can be performed elegantly 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.

AB - 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 nontrivial analytic continuation which, in the framework of CFT, can be performed elegantly 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.

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U2 - 10.1016/j.nuclphysb.2014.04.020

DO - 10.1016/j.nuclphysb.2014.04.020

M3 - Article

AN - SCOPUS:84900410256

SN - 0550-3213

VL - 884

SP - 305

EP - 343

JO - Nuclear Physics B

JF - Nuclear Physics B

IS - 1

ER -