TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.15.3.098
TI  - Internal boundaries of the loop amplituhedron
PY  - 2023/09/18
UR  - https://scipost.org/SciPostPhys.15.3.098
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 15
IS  - 3
SP  - 098
A1  - Dian, Gabriele
AU  - Heslop, Paul
AU  - Stewart, Alastair
AB  - The strict definition of positive geometry implies that all maximal residues of its canonical form are $± 1$. We observe, however, that the loop integrand of the amplitude in planar ${\cal N}=4$ super Yang-Mills has maximal residues not equal to $± 1$. We find the reason for this is that deep in the boundary structure of the loop amplituhedron there are geometries which contain internal boundaries: codimension one defects separating two regions of opposite orientation. This phenomenon requires a generalisation of the concept of positive geometry and canonical form to include such internal boundaries and also suggests the utility of a further generalisation to `weighted positive geometries'. We re-examine the deepest cut of ${\cal N}=4$ amplitudes in light of this and obtain new all order residues.
ER  -

@Article{10.21468/SciPostPhys.15.3.098,
	title={{Internal boundaries of the loop amplituhedron}},
	author={Gabriele Dian and Paul Heslop and Alastair Stewart},
	journal={SciPost Phys.},
	volume={15},
	pages={098},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.15.3.098},
	url={https://scipost.org/10.21468/SciPostPhys.15.3.098},
}