Bootstrapping correlation functions in N=4 SYM

TL;DR

This paper introduces a symmetry-based method to compute correlation functions in N=4 SYM, fixing their form through invariants and asymptotic limits, and applies it to six-point functions and amplitudes.

Contribution

It presents a novel approach relying solely on symmetries and analytic properties to determine correlation functions and amplitudes without gauge fixing or spurious poles.

Findings

Six-point correlation function fixed up to four constants in Born approximation

Asymptotic light-like limit determines coefficients unambiguously

Method yields gauge-parameter-free, dual superconformal invariant amplitude representation

Abstract

We describe a new approach to computing the chiral part of correlation functions of stress-tensor supermultiplets in N=4 SYM that relies on symmetries, analytic properties and the structure of the OPE only. We demonstrate that the correlation functions are given by a linear combination of chiral N=4 superconformal invariants accompanied by coefficient functions depending on the space-time coordinates only. We present the explicit construction of these invariants and show that the six-point correlation function is fixed in the Born approximation up to four constant coefficients by its symmetries. In addition, the known asymptotic structure of the correlation function in the light-like limit fixes unambiguously these coefficients up to an overall normalization. We demonstrate that the same approach can be applied to obtain a representation for the six-point NMHV amplitude that is free from any auxiliary gauge fixing parameters, does not involve spurious poles and manifests half of the dual superconformal symmetry.