Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 1, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP01(2016)112
Keywords
Scattering Amplitudes; Supersymmetric gauge theory; Differential and Algebraic Geometry
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Funding
- Department of Physics, Princeton University
- Institute of Theoretical Physics, Chinese Academy of Science, China
- NSF [DMS-1160726, DMS-1464693]
- Simons Fellowship [341949]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1464693] Funding Source: National Science Foundation
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All-loop planar scattering amplitudes in maximally supersymmetric Yang-Mills theory can be formulated geometrically in terms of the amplituhedron. We study the mathematical structures of the one-loop amplituhedron, and present a new formula for its canonical measure, or the one-loop Grassmannian measure formula. Using the recently proposed momentum-twistor diagrams, we show that there is a correspondence between the cells of one-loop amplituhedron, BCFW terms or equivalently on-shell diagrams, and residues of the one-loop Grassmannian formula. In particular, for the first non-trivial case of one-loop NMHV, these structures are naturally associated with a nice geometric picture as polygons in projective space, as we discuss in various illustrative examples.
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