Descent equations for superamplitudes

TL;DR

This paper investigates the breaking of dual superconformal symmetry in planar N=4 super Yang-Mills at loop level, introducing descent equations that relate amplitudes across loop orders to facilitate their recursive construction.

Contribution

It introduces descent equations that connect L-loop amplitudes to (L-1)-loop amplitudes, providing a recursive method to construct multi-loop superamplitudes with manifest transcendentality.

Findings

The dual superconformal symmetry is broken at loop level due to an anomaly.

A descent equation controls the derivative of L-loop amplitudes in terms of (L-1)-loop amplitudes.

Recursive construction of multi-loop amplitudes is possible using the descent equations.

Abstract

At loop level in planar N=4 super Yang-Mills, the dual superconformal symmetry of tree amplitudes is lost. This is true even if one uses a supersymmetry preserving regulator, and even for finite quantities that remain dual conformally invariant. We examine this breaking from the dual point of view of the super Wilson Loop, tracing it to the difference between supersymmetries of the self-dual and of the full theories. We show that the anomaly is controlled by a descent equation that determines the derivative of an L-loop amplitude in terms of a single non-trivial integral of an (L-1)-loop amplitude. We propose that this equation can be used recursively to construct multi-loop amplitudes in a way that makes their transcendentality manifest.