Anatomy of the amplituhedron

Franco, Sebastián; Galloni, Daniele; Mariotti, Alberto; Trnka, Jaroslav

doi:10.1007/JHEP03(2015)128

Title: Anatomy of the amplituhedron

Journal Article · Tue Mar 24 00:00:00 EDT 2015 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP03(2015)128· OSTI ID:1596492

Franco, Sebastián ^[1]; Galloni, Daniele ^[1]; Mariotti, Alberto ^[1]; Trnka, Jaroslav ^[2]

Durham Univ. (United Kingdom)
California Inst. of Technology (CalTech), Pasadena, CA (United States)

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 $ \mathcal{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.

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Research Organization:: California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP); UK Science and Technology Facilities Council (STFC)

Grant/Contract Number:: SC0011632; FG03-92ER40701

OSTI ID:: 1596492

Journal Information:: Journal of High Energy Physics (Online), Vol. 2015, Issue 3; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 40 works

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References (41)

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Four-dimensional ambitwistor strings and form factors of local and Wilson line operators Bork, L. V.; Onishchenko, A. I. Physical Review D, Vol. 97, Issue 12 https://doi.org/10.1103/physrevd.97.126013	journal	June 2018
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All-loop cuts from the Amplituhedron Langer, Cameron; Srikant, Akshay Yelleshpur Journal of High Energy Physics, Vol. 2019, Issue 4 https://doi.org/10.1007/jhep04(2019)105	journal	April 2019
Wilson lines, Grassmannians and gauge invariant off-shell amplitudes in N = 4 $$ \mathcal{N}=4 $$ SYM Bork, L. V.; Onishchenko, A. I. Journal of High Energy Physics, Vol. 2017, Issue 4 https://doi.org/10.1007/jhep04(2017)019	journal	April 2017
On-shell diagrams and the geometry of planar N < 4 $$ \mathcal{N}<4 $$ SYM theories Benincasa, Paolo; Gordo, David Journal of High Energy Physics, Vol. 2017, Issue 11 https://doi.org/10.1007/jhep11(2017)192	journal	November 2017
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Gravity On-shell Diagrams Herrmann, Enrico; Trnka, Jaroslav arXiv https://doi.org/10.48550/arxiv.1604.03479	text	January 2016
Four dimensional ambitwistor strings and form factors of local and Wilson line operators Bork, L. V.; Onishchenko, A. I. arXiv https://doi.org/10.48550/arxiv.1704.04758	text	January 2017
Prescriptive Unitarity Bourjaily, Jacob L.; Herrmann, Enrico; Trnka, Jaroslav arXiv https://doi.org/10.48550/arxiv.1704.05460	text	January 2017
All-Helicity Symbol Alphabets from Unwound Amplituhedra Prlina, Igor; Spradlin, Marcus; Stankowicz, James arXiv https://doi.org/10.48550/arxiv.1711.11507	text	January 2017
All-loop cuts from the Amplituhedron Langer, Cameron; Srikant, Akshay Yelleshpur arXiv https://doi.org/10.48550/arxiv.1902.05951	text	January 2019

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