Anatomy of the Amplituhedron
Abstract
We initiate a comprehensive investigation of the geometry of the amplituhedron, a recently found geometric object whose volume calculates the integrand of scattering amplitudes in planar N=4 SYM theory. We do so by introducing and studying its stratification, focusing on four-point amplitudes. The new stratification exhibits interesting combinatorial properties and positivity is neatly captured by permutations. As explicit examples, we find all boundaries for the two and three loop amplitudes and related geometries. We recover the stratifications of some of these geometries from the singularities of the corresponding integrands, providing a non-trivial test of the amplituhedron/scattering amplitude correspondence. We finally introduce a deformation of the stratification with remarkably simple topological properties.
Additional Information
© 2015 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Received: February 3, 2015; Accepted: February 28, 2015; Published: March 24, 2015. We would like to thank N. Arkani-Hamed for very useful discussions. D. G. would like to thank the Simons Summer Workshop at the Simons Center for Geometry and Physics for hospitality during the completion of this work. The work of S. F. and D. G. is supported by the U.K. Science and Technology Facilities Council (STFC). A.M. acknowledges funding by the Durham International Junior Research Fellowship. J. T. is supported in part by the David and Ellen Lee Postdoctoral Scholarship and by DOE grant DE-FG03-92-ER40701.Attached Files
Published - art_10.1007_JHEP03_2015_128.pdf
Submitted - 1408.3410.pdf
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Additional details
- Eprint ID
- 48850
- Resolver ID
- CaltechAUTHORS:20140825-123237108
- Science and Technology Facilities Council (STFC)
- Durham International Junior Research Fellowship
- David and Ellen Lee Postdoctoral Scholarship
- Department of Energy (DOE)
- DE-FG03-92-ER40701
- Created
-
2014-08-25Created from EPrint's datestamp field
- Updated
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2021-11-10Created from EPrint's last_modified field
- Caltech groups
- Walter Burke Institute for Theoretical Physics
- Other Numbering System Name
- CALT-TH
- Other Numbering System Identifier
- 2014-152