One-Loop Amplitudes in N=4 Super Yang-Mills and Anomalous Dual Conformal Symmetry

TL;DR

This paper explores how anomalous dual conformal symmetry constrains one-loop superamplitudes in N=4 super Yang-Mills theory, revealing new relations among supercoefficients and confirming covariance of NMHV amplitudes.

Contribution

It introduces novel relations among supercoefficients derived from anomalous dual conformal symmetry and proves covariance of NMHV superamplitudes at any number of points.

Findings

Anomaly coefficient is a combination of supercoefficients equal to the tree-level superamplitude.

All one-loop supercoefficients except four-mass box can be expressed via three-mass and two-mass hard coefficients.

Explicit verification for n-point MHV and NMHV amplitudes confirms the derived relations.

Abstract

We discuss what predictions can be made for one-loop superamplitudes in maximally supersymmetric Yang-Mills theory by using anomalous dual conformal symmetry. We show that the anomaly coefficient is a specific combination of two-mass hard and one-mass supercoefficients which appears in the supersymmetric on-shell recursion relations and equals the corresponding tree-level superamplitude. We discuss further novel relations among supercoefficients imposed by the remaining non-anomalous part of the symmetry. In particular, we find that all one-loop supercoefficients, except the four-mass box coefficients, can be expressed as linear combinations of three-mass box coefficients and a particular symmetric combination of two-mass hard coefficients. We check that our equations are explicitly satisfied in the case of one-loop n-point MHV and NMHV amplitudes. As a bonus, we prove the covariance of the NMHV superamplitudes at an arbitrary number of points, extending previous results at n <= 9.