Event shapes in N=4 super-Yang-Mills theory

TL;DR

This paper computes and analyzes event shapes in N=4 super-Yang-Mills theory using correlation functions, revealing simple relations from superconformal symmetry and confirming results at weak and strong coupling.

Contribution

It introduces a unified approach to calculate event shapes in N=4 SYM via correlation functions and Mellin amplitudes, connecting weak and strong coupling regimes.

Findings

Derived all-order formulas for event shapes as convolutions with Mellin amplitudes.

Found simple relations between different event shapes from superconformal symmetry.

Confirmed weak coupling results and extended analysis to strong coupling via AdS/CFT.

Abstract

We study event shapes in N=4 SYM describing the angular distribution of energy and R-charge in the final states created by the simplest half-BPS scalar operator. Applying the approach developed in the companion paper arXiv:1309.0769, we compute these observables using the correlation functions of certain components of the N=4 stress-tensor supermultiplet: the half-BPS operator itself, the R-symmetry current and the stress tensor. We present master formulas for the all-order event shapes as convolutions of the Mellin amplitude defining the correlation function of the half-BPS operators, with a coupling-independent kernel determined by the choice of the observable. We find remarkably simple relations between various event shapes following from N=4 superconformal symmetry. We perform thorough checks at leading order in the weak coupling expansion and show perfect agreement with the conventional calculations based on amplitude techniques. We extend our results to strong coupling using the correlation function of half-BPS operators obtained from the AdS/CFT correspondence.