Multi-loop positivity of the planar N = 4 SYM six-point amplitude
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We study the six-point NMHV ratio function in planar 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.
Originalsprog | Engelsk |
---|---|
Artikelnummer | 112 |
Tidsskrift | Journal of High Energy Physics |
Vol/bind | 2017 |
Udgave nummer | 2 |
Antal sider | 40 |
ISSN | 1126-6708 |
DOI | |
Status | Udgivet - 1 feb. 2017 |
Eksternt udgivet | Ja |
ID: 279625400