More on the duality correlators/amplitudes

TL;DR

The authors provide convincing evidence for a new duality between light-like correlators of half-BPS operators with Lagrangian insertions and the integrands of MHV amplitudes in planar N=4 SYM, examined through both a correlation-function framework and a momentum-twistor formulation. They establish exact one-loop equivalence (up to a simple factor) and verify, up to two loops, that the light-cone correlator integrands satisfy precise relations with the twistor amplitude integrands for n=4,5,6, including parity-odd contributions. The results extend beyond a formal analogy by presenting explicit expressions and numerical checks (notably at five points and six points), suggesting a deeper structural connection between correlators with insertions and amplitude integrands. The work points to future goals of generalizing to non-MHV cases and uncovering the fundamental mechanism behind this duality, potentially linking correlators, Wilson loops, and scattering amplitudes in a unified framework.

Abstract

We continue the study of n-point correlation functions 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 l-loop corrections by making l Lagrangian insertions. We argue that there exists a simple relation between the (n+l)-point tree-level correlator with l Lagrangian insertions and the integrand of the n-particle l-loop MHV scattering amplitude, as obtained by the recent momentum twistor construction of Arkani-Hamed et al. We present several examples of this new duality, at one and two loops.

Figures (1)

• Figure 1: Graphs contributing to the six-point correlator on the light cone