Into the amplituhedron
Abstract
We initiate an exploration of the physics and geometry of the amplituhedron, starting with the simplest case of the integrand for four-particle scattering in planar \( \mathcal{N}=4 \) SYM. We show how the textbook structure of the unitarity double-cut follows from the positive geometry. We also use the geometry to expose the behavior of the multicollinear limit, providing a direct motivation for studying the logarithm of the amplitude. In addition to computing the two and three-loop integrands, we explore various lower-dimensional faces of the amplituhedron, thereby computing non-trivial cuts of the integrand to all loop orders.
- Authors:
-
- Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences
- California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics
- Publication Date:
- Research Org.:
- Institute for Advanced Study, Princeton, NJ (United States); Harvard Univ., Cambridge, MA (United States); California Institute of Technology (CalTech), Pasadena, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF)
- OSTI Identifier:
- 1598502
- Grant/Contract Number:
- SC0009988; FG02-91ER40654; FG03-92ER40701; PHY-0756966
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of High Energy Physics (Online)
- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2014; Journal Issue: 12; Journal ID: ISSN 1029-8479
- Publisher:
- Springer Berlin
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; supersymmetry: 4; geometry; scattering; unitarity; supersymmetric gauge theory; scattering amplitudes
Citation Formats
Arkani-Hamed, Nima, and Trnka, Jaroslav. Into the amplituhedron. United States: N. p., 2014.
Web. doi:10.1007/JHEP12(2014)182.
Arkani-Hamed, Nima, & Trnka, Jaroslav. Into the amplituhedron. United States. https://doi.org/10.1007/JHEP12(2014)182
Arkani-Hamed, Nima, and Trnka, Jaroslav. Wed .
"Into the amplituhedron". United States. https://doi.org/10.1007/JHEP12(2014)182. https://www.osti.gov/servlets/purl/1598502.
@article{osti_1598502,
title = {Into the amplituhedron},
author = {Arkani-Hamed, Nima and Trnka, Jaroslav},
abstractNote = {We initiate an exploration of the physics and geometry of the amplituhedron, starting with the simplest case of the integrand for four-particle scattering in planar \( \mathcal{N}=4 \) SYM. We show how the textbook structure of the unitarity double-cut follows from the positive geometry. We also use the geometry to expose the behavior of the multicollinear limit, providing a direct motivation for studying the logarithm of the amplitude. In addition to computing the two and three-loop integrands, we explore various lower-dimensional faces of the amplituhedron, thereby computing non-trivial cuts of the integrand to all loop orders.},
doi = {10.1007/JHEP12(2014)182},
journal = {Journal of High Energy Physics (Online)},
number = 12,
volume = 2014,
place = {United States},
year = {Wed Dec 31 00:00:00 EST 2014},
month = {Wed Dec 31 00:00:00 EST 2014}
}
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