From correlation functions to scattering amplitudes

TL;DR

This paper establishes a precise relation between light-like limit correlators of protected operators in N=4 super-Yang-Mills theory and gluon scattering amplitudes, revealing a deep connection in the structure of quantum field theory.

Contribution

It demonstrates that the logarithm of certain correlators equals twice the logarithm of MHV gluon scattering amplitudes, providing new insights into their equivalence at loop levels.

Findings

Logarithm of correlator equals twice the logarithm of scattering amplitude.

Relation verified at one and two loops.

Divergences regularized by changing integration measure dimension.

Abstract

We study the correlators of half-BPS protected operators in N=4 super-Yang-Mills theory, in the limit where the positions of the adjacent operators become light-like separated. We compute the loop corrections by means of Lagrangian insertions. The divergences resulting from the light-cone limit are regularized by changing the dimension of the integration measure over the insertion points. Switching from coordinates to dual momenta, we show that the logarithm of the correlator is identical with twice the logarithm of the matching MHV gluon scattering amplitude. We present a number of examples of this new relation, at one and two loops.