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SUMMARY:Positive Geometry\, local triangulations and the dual of the Ampli
tuhedron
DTSTART;VALUE=DATE-TIME:20210624T143000Z
DTEND;VALUE=DATE-TIME:20210624T153000Z
DTSTAMP;VALUE=DATE-TIME:20210925T032911Z
UID:indico-event-6880@indico.ph.tum.de
DESCRIPTION:We initiate the systematic study of local positive spaces whic
h arise in the context of the Amplituhedron for scattering amplitudes in p
lanar maximally supersymmetric Yang-Mills theory. We show that all local p
ositive spaces relevant for one-loop MHV amplitudes are characterized by c
ertain sign-flip conditions and are associated with surprisingly simple lo
garithmic forms. In the maximal sign-flip case they are finite one-loop oc
tagons. Particular combinations of sign-flip spaces can be glued into new
local positive geometries. These correspond to local pentagon integrands t
hat appear in the local expansion of the MHV one-loop amplitude. We show t
hat\, geometrically\, these pentagons do not triangulate the original Ampl
ituhedron space but rather its twin "Amplituhedron-Prime." This new geomet
ry has the same boundary structure as the Amplituhedron (and therefore the
same logarithmic form) but differs in the bulk as a geometric space. Inte
restingly\, we find that the pentagons internally triangulate that dual sp
ace. This gives direct evidence that the chiral pentagons are natural buil
ding blocks for a yet-to-be discovered dual Amplituhedron.\n\nhttps://indi
co.ph.tum.de/event/6880/
LOCATION:Zoom
URL:https://indico.ph.tum.de/event/6880/
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