Aspects of the N=4 SYM amplitude -- Wilson polygon duality

TL;DR

This paper explores the duality between Wilson polygons and MHV amplitudes in N=4 SYM theory, providing a perturbative formulation that interpolates regularizations and reveals new geometric and nullification phenomena.

Contribution

It introduces a diagrammatic correspondence between regularizations and offers a novel geometric interpretation of box diagrams in terms of dual simplexes.

Findings

One-loop interpolation between dimensional and off-shell regularizations.

New geometric interpretation of box diagrams as dual simplexes.

Nullification phenomena in low-energy Higgsed phase amplitudes.

Abstract

We discuss formulation of Wilson polygon - MHV amplitude duality at the perturbative level in various regularizations. For four gluons it is shown that at one loop one can formulate diagrammatic correspondence interpolating between the dimensional regularization and the off-shell one. We suggest new interpretation of all types of box diagrams in terms of the dual simplex in dimensional regularization and describe its degeneration to the Wilson polygon. The interesting nullification phenomena for the low-energy amplitudes in the Higgsed phase has been found.