Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 4, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP04(2012)081
Keywords
Scattering Amplitudes; Duality in Gauge Field Theories
Categories
Funding
- DOE [DE-FG02-91ER40654]
- NSERC of Canada
- MEDT of Ontario
- Ambrose Monell Foundation
- U.S. Department of State
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In this note we continue the exploration of the polytope picture for scattering amplitudes, where amplitudes are associated with the volumes of polytopes in generalized momentum-twistor spaces. After a quick warm-up example illustrating the essential ideas with the elementary geometry of polygons in CP2, we interpret the 1-loop MHV integrand as the volume of a polytope in CP3 x CP3, which can be thought of as the space obtained by taking the geometric dual of the Wilson loop in each CP3 of the product. We then review the polytope picture for the NMHV tree amplitude and give it a more direct and intrinsic definition as the geometric dual of a canonical square of the Wilson-Loop polygon, living in a certain extension of momentum-twistor space into CP4. In both cases, one natural class of triangulations of the polytope produces the BCFW/CSW representations of the amplitudes; another class of triangulations leads to a striking new form, which is both remarkably simple as well as manifestly cyclic and local.
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