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  All-loop Mondrian reduction of 4-particle amplituhedron at positive infinity

Rao, J. (2020). All-loop Mondrian reduction of 4-particle amplituhedron at positive infinity. Nuclear Physics B, 957: 115086. doi:10.1016/j.nuclphysb.2020.115086.

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Item Permalink: http://hdl.handle.net/21.11116/0000-0005-4D0B-A Version Permalink: http://hdl.handle.net/21.11116/0000-0006-9715-8
Genre: Journal Article

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 Creators:
Rao, Junjie1, Author              
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1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014              

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Free keywords: High Energy Physics - Theory, hep-th
 Abstract: This article introduces a systematic framework to understand (not to derive yet) the all-loop 4-particle amplituhedron in planar N=4 SYM, utilizing both positivity and the Mondrian diagrammatics. Its key idea is the simplest one so far: we can decouple one or more sets of loop variables (x,y,z,w) from the rest by just setting these variables to either zero or infinity so that their relevant positivity conditions are trivialized, then the all-loop consistency requires that we get lower loop amplituhedra as "residues". These decoupling relations connect higher loop DCI integrals with the lower ones, enabling us to identify their coefficients starting from the 3-loop case. And surprisingly, the delicate mechanism of this process is the simple Mondrian rule D=X+Y, which forces those visually non-Mondrian DCI integrals to have the correct coefficients such that the amplituhedron can exactly reduce to the lower loop one. Examples cover all DCI integrals at L=3,4,5,6, especially, the subtle 6-loop coefficients +2 and 0 are neatly explained in this way.

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 Dates: 2019-10-312020
 Publication Status: Published in print
 Pages: 16 pages, 13 figures
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 Table of Contents: -
 Rev. Type: -
 Identifiers: arXiv: 1910.14612
URI: http://arxiv.org/abs/1910.14612
DOI: 10.1016/j.nuclphysb.2020.115086
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Title: Nuclear Physics B
Source Genre: Journal
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Pages: - Volume / Issue: 957 Sequence Number: 115086 Start / End Page: - Identifier: -