Multi-Loop Positivity of the Planar ${\cal N}=4$ SYM Six-Point Amplitude

Andrew J. McLeod; Jaroslav Trnka; Lance J. Dixon; Matt von Hippel

Multi-Loop Positivity of the Planar {cal N}=4 SYM Six-Point Amplitude

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1611.08325 v2 pith:ETLO6TU7 submitted 2016-11-25 hep-th

Multi-Loop Positivity of the Planar {cal N}=4 SYM Six-Point Amplitude

Lance J. Dixon , Matt von Hippel , Andrew J. McLeod , Jaroslav Trnka This is my paper

classification hep-th

keywords positivefunctionloopspositivityamplituderatioevidencefive

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

0 comments

read the original abstract

We study the six-point NMHV ratio function in planar ${\cal N}=4$ SYM theory in the context of positive geometry. The Amplituhedron construction of the integrand for the amplitudes provides a kinematical region in which the integrand was observed to be positive. It is natural to conjecture that this property survives integration, i.e. that the final result for the ratio function is also positive in this region. Establishing such a result would imply that preserving positivity is a surprising property of the Minkowski contour of integration and it might indicate some deeper underlying structure. We find that the ratio function is positive everywhere we have tested it, including analytic results for special kinematical regions at one and two loops, as well as robust numerical evidence through five loops. There is also evidence for not just positivity, but monotonicity in a "radial" direction. We also investigate positivity of the MHV six-gluon amplitude. While the remainder function ceases to be positive at four loops, the BDS-like normalized MHV amplitude appears to be positive through five loops.

discussion (0)

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

Landau Analysis of One-Cycle Negative Geometries
hep-th 2026-04 unverdicted novelty 7.0

One-cycle negative geometries in N=4 SYM have singularities only at z=-1, 0, and infinity to all loop orders.
Form factors of $\mathscr{N}=4$ self-dual Yang-Mills from the chiral algebra bootstrap
hep-th 2026-04 conditional novelty 7.0

The chiral algebra bootstrap yields all-loop splitting functions for self-dual N=4 SYM, a proof of no double-pole OPEs, and novel two-loop form factors with anti-self-dual field strength insertions.