The ${\cal N}=4$ Supergravity NMHV six-point one-loop amplitude

TL;DR

The paper delivers the six-point NMHV one-loop amplitude for $\\mathcal{N}=4$ supergravity by combining unitarity cuts with on-shell recursion, explicitly handling the rational piece $R_6$ via rational descendants. It systematically constructs cut-constructible contributions from boxes, triangles, and bubbles, employs IR-consistency to fix coefficients, and uses a truncated box basis to absorb IR-divergent pieces. A canonical-basis framework is developed to extract triangle and bubble coefficients from two- and three-particle cuts, with KLT relations aiding three-mass triangle calculations. The work also confronts higher-order and spurious poles, deriving RD terms and addressing non-standard factorisations for complex momenta, culminating in a complete, symmetry-respecting expression for $R_6$ and providing a Mathematica implementation. Together, these results illuminate the structure of non-MHV amplitudes in less-than-maximal supergravity and demonstrate techniques to manage their intricate rational content.

Abstract

We construct the six-point NMHV one-loop amplitude in ${\cal N}=4$ supergravity using unitarity and recursion. The use of recursion requires the introduction of rational descendants of the cut-constructible pieces of the amplitude and the computation of the non-standard factorisation terms arising from the loop integrals.

Figures (5)

• Figure 1: The Integral functions appearing in the six-point NMHV amplitude
• Figure 2: A two-particle cut of a one-loop amplitude
• Figure 3: Triple Cut
• Figure 4: Non-standard factorisations channel
• Figure 5: The box integrals associated with \ref{['boxexample']}