Cross-Order Relations in N=4 Supersymmetric Gauge Theories

TL;DR

The paper investigates whether the perturbative expansion in N=4 SYM can be organized into simple, resummed structures as suggested by AdS/CFT. It uses unitarity-based methods to construct on-shell amplitudes and derives a specific relation between the one-loop and two-loop planar four-point amplitudes, namely M4^(2)(ε) = 1/2 [M4^(1)(ε)]^2 + f(ε) M4^(1)(2ε) - 5/4 zeta4, with the finite part consistent with known infrared behavior. The authors test this relation in collinear limits and argue that similar relations should hold for higher-point and higher-loop amplitudes, guided by the structure of infrared divergences and the leading-color (planar) limit, hinting at an underlying symmetry perhaps tied to superconformal invariance. These findings suggest a pathway to understanding AdS/CFT duality from on-shell amplitudes and may have implications for higher-loop gravity theories.

Abstract

The anti-de Sitter/conformal field theory duality conjecture raises the question of how the perturbative expansion in the conformal field theory can resum to a simple function. We exhibit a relation between the one-loop and two-loop amplitudes whose generalization to higher-point and higher-loop amplitudes would answer this question. We also provide evidence for the first of these generalizations.