Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory

TL;DR

This paper reveals a new dual superconformal symmetry in N=4 super-Yang-Mills scattering amplitudes, formulated in dual superspace, with implications for both tree-level and loop-level calculations.

Contribution

It introduces dual superconformal symmetry in scattering amplitudes and provides a compact formula for NMHV amplitudes, extending the understanding of symmetries in N=4 SYM.

Findings

Tree-level MHV and NMHV amplitudes exhibit manifest dual superconformal symmetry.

The ratio of MHV to NMHV superamplitudes is dual conformal invariant.

Explicit one-loop six-particle amplitude calculations support the conjecture.

Abstract

We argue that the scattering amplitudes in the maximally supersymmetric N=4 super-Yang-Mills theory possess a new symmetry which extends the previously discovered dual conformal symmetry. To reveal this property we formulate the scattering amplitudes as functions in the appropriate dual superspace. Rewritten in this form, all tree-level MHV and next-to-MHV amplitudes exhibit manifest dual superconformal symmetry. We propose a new, compact and Lorentz covariant formula for the tree-level NMHV amplitudes for arbitrary numbers and types of external particles. The dual conformal symmetry is broken at loop level by infrared divergences. However, we provide evidence that the anomalous contribution to the MHV and NMHV superamplitudes is the same and, therefore, their ratio is a dual conformal invariant function. We identify this function by an explicit calculation of the six-particle amplitudes at one loop. We conjecture that these properties hold for all, MHV and non-MHV, superamplitudes in N=4 SYM both at weak and at strong coupling.