Into the amplituhedron

Arkani-Hamed, Nima; Trnka, Jaroslav

doi:10.1007/JHEP12(2014)182

Title: Into the amplituhedron

Journal Article · Wed Dec 31 00:00:00 EST 2014 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP12(2014)182· OSTI ID:1598502

Arkani-Hamed, Nima ^[1]; Trnka, Jaroslav ^[2]

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

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.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Institute for Advanced Study, Princeton, NJ (United States); Harvard Univ., Cambridge, MA (United States); California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF)

Grant/Contract Number:: SC0009988; FG02-91ER40654; FG03-92ER40701; PHY-0756966

OSTI ID:: 1598502

Journal Information:: Journal of High Energy Physics (Online), Vol. 2014, Issue 12; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 96 works

Citation information provided by
Web of Science

References (12)

The SYM integrable super spin chain Beisert, Niklas; Staudacher, Matthias Nuclear Physics B, Vol. 670, Issue 3 https://doi.org/10.1016/j.nuclphysb.2003.08.015	journal	October 2003
The Amplituhedron Arkani-Hamed, Nima; Trnka, Jaroslav Journal of High Energy Physics, Vol. 2014, Issue 10 https://doi.org/10.1007/JHEP10(2014)030	journal	October 2014
Gluon scattering amplitudes at strong coupling Alday, Luis F.; Maldacena, Juan Journal of High Energy Physics, Vol. 2007, Issue 06 https://doi.org/10.1088/1126-6708/2007/06/064	journal	June 2007
Eliminating spurious poles from gauge-theoretic amplitudes Hodges, Andrew Journal of High Energy Physics, Vol. 2013, Issue 5 https://doi.org/10.1007/JHEP05(2013)135	journal	May 2013
Harmonic $R$ Matrices for Scattering Amplitudes and Spectral Regularization Ferro, Livia; Łukowski, Tomasz; Meneghelli, Carlo Physical Review Letters, Vol. 110, Issue 12 https://doi.org/10.1103/PhysRevLett.110.121602	journal	March 2013
The all-loop integrand for scattering amplitudes in planar $ \mathcal{N} = 4 $ SYM Arkani-Hamed, N.; Bourjaily, J.; Cachazo, F. Journal of High Energy Physics, Vol. 2011, Issue 1 https://doi.org/10.1007/JHEP01(2011)041	journal	January 2011
A duality for the S matrix Arkani-Hamed, N.; Cachazo, F.; Cheung, C. Journal of High Energy Physics, Vol. 2010, Issue 3 https://doi.org/10.1007/JHEP03(2010)020	journal	March 2010
The soft-collinear bootstrap: $ \mathcal{N} = {4} $ Yang-Mills amplitudes at six- and seven-loops Bourjaily, J. L.; DiRe, A.; Shaikh, A. Journal of High Energy Physics, Vol. 2012, Issue 3 https://doi.org/10.1007/JHEP03(2012)032	journal	March 2012
Constructing the correlation function of four stress-tensor multiplets and the four-particle amplitude in SYM Eden, Burkhard; Heslop, Paul; Korchemsky, Gregory P. Nuclear Physics B, Vol. 862, Issue 2 https://doi.org/10.1016/j.nuclphysb.2012.04.013	journal	September 2012
Loops and trees Caron-Huot, S. Journal of High Energy Physics, Vol. 2011, Issue 5 https://doi.org/10.1007/JHEP05(2011)080	journal	May 2011
Direct Proof of the Tree-Level Scattering Amplitude Recursion Relation in Yang-Mills Theory Britto, Ruth; Cachazo, Freddy; Feng, Bo Physical Review Letters, Vol. 94, Issue 18 https://doi.org/10.1103/PhysRevLett.94.181602	journal	May 2005
Local integrals for planar scattering amplitudes Arkani-Hamed, N.; Bourjaily, J.; Cachazo, F. Journal of High Energy Physics, Vol. 2012, Issue 6 https://doi.org/10.1007/JHEP06(2012)125	journal	June 2012

Cited By (31)

UV cancellations in gravity loop integrands Herrmann, Enrico; Trnka, Jaroslav Journal of High Energy Physics, Vol. 2019, Issue 2 https://doi.org/10.1007/jhep02(2019)084	journal	February 2019
The all-loop conjecture for integrands of reggeon amplitudes in N = 4 $$ \mathcal{N}=4 $$ SYM Bolshov, A. E.; Bork, L. V.; Onishchenko, A. I. Journal of High Energy Physics, Vol. 2018, Issue 6 https://doi.org/10.1007/jhep06(2018)129	journal	June 2018
Heptagons from the Steinmann Cluster Bootstrap Dixon, Lance J.; Drummond, James; Harrington, Thomas Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2017-00889	text	January 2017
Accordiohedra as positive geometries for generic scalar field theories Aneesh, P. B.; Jagadale, Mrunmay; Kalyanapuram, Nikhil Physical Review D, Vol. 100, Issue 10 https://doi.org/10.1103/physrevd.100.106013	journal	November 2019
On-shell diagrams for N $$ \mathcal{N} $$ = 8 supergravity amplitudes Heslop, Paul; Lipstein, Arthur E. Journal of High Energy Physics, Vol. 2016, Issue 6 https://doi.org/10.1007/jhep06(2016)069	journal	June 2016
Positivity, Grassmannian geometry and simplex-like structures of scattering amplitudes Rao, Junjie Journal of High Energy Physics, Vol. 2017, Issue 12 https://doi.org/10.1007/jhep12(2017)147	journal	December 2017
The Sklyanin bracket and cluster adjacency at all multiplicity Golden, John; McLeod, Andrew J.; Spradlin, Marcus Journal of High Energy Physics, Vol. 2019, Issue 3 https://doi.org/10.1007/jhep03(2019)195	journal	March 2019
Amplituhedron meets Jeffrey–Kirwan residue Ferro, Livia; Łukowski, Tomasz; Parisi, Matteo Journal of Physics A: Mathematical and Theoretical, Vol. 52, Issue 4 https://doi.org/10.1088/1751-8121/aaf3c3	journal	December 2018
Properties of scattering forms and their relation to associahedra de la Cruz, Leonardo; Kniss, Alexander; Weinzierl, Stefan Journal of High Energy Physics, Vol. 2018, Issue 3 https://doi.org/10.1007/jhep03(2018)064	journal	March 2018
Non-planar on-shell diagrams Franco, Sebastián; Galloni, Daniele; Penante, Brenda Journal of High Energy Physics, Vol. 2015, Issue 6 https://doi.org/10.1007/jhep06(2015)199	journal	June 2015
A periodic table of effective field theories Cheung, Clifford; Kampf, Karol; Novotny, Jiri Journal of High Energy Physics, Vol. 2017, Issue 2 https://doi.org/10.1007/jhep02(2017)020	journal	February 2017
Orientations of BCFW charts on the Grassmannian Olson, Timothy M. Journal of High Energy Physics, Vol. 2015, Issue 8 https://doi.org/10.1007/jhep08(2015)120	journal	August 2015
Six-Gluon Amplitudes in Planar ${\cal N}=4$ Super-Yang-Mills Theory at Six and Seven Loops Caron-Huot, Simon; Dixon, Lance J.; Dulat, Falko Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2019-01783	text	January 2019
The double pentaladder integral to all ordersC Caron-Huot, Simon; Dixon, Lance J.; Von Hippel, Matt Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2018-05437	text	January 2018
Orientations of BCFW Charts on the Grassmannian Olson, Timothy M. arXiv https://doi.org/10.48550/arxiv.1411.6363	preprint	January 2014
Logarithmic Singularities and Maximally Supersymmetric Amplitudes Bern, Zvi; Herrmann, Enrico; Litsey, Sean arXiv https://doi.org/10.48550/arxiv.1412.8584	preprint	January 2014
Non-Planar On-Shell Diagrams Franco, Sebastian; Galloni, Daniele; Penante, Brenda arXiv https://doi.org/10.48550/arxiv.1502.02034	preprint	January 2015
Local Integrand Representations of All Two-Loop Amplitudes in Planar SYM Bourjaily, Jacob L.; Trnka, Jaroslav arXiv https://doi.org/10.48550/arxiv.1505.05886	text	January 2015
Evidence for a Nonplanar Amplituhedron Bern, Zvi; Herrmann, Enrico; Litsey, Sean arXiv https://doi.org/10.48550/arxiv.1512.08591	text	January 2015
Gravity On-shell Diagrams Herrmann, Enrico; Trnka, Jaroslav arXiv https://doi.org/10.48550/arxiv.1604.03479	text	January 2016
Heptagons from the Steinmann Cluster Bootstrap Dixon, Lance J.; Drummond, James; Harrington, Thomas arXiv https://doi.org/10.48550/arxiv.1612.08976	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
Combinatorics and Topology of Kawai-Lewellen-Tye Relations Mizera, Sebastian arXiv https://doi.org/10.48550/arxiv.1706.08527	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
Boundaries of Amplituhedra and NMHV Symbol Alphabets at Two Loops Prlina, Igor; Spradlin, Marcus; Stankowicz, James arXiv https://doi.org/10.48550/arxiv.1712.08049	text	January 2017
4-particle Amplituhedron at 3-loop and its Mondrian Diagrammatic Implication Rao, Junjie arXiv https://doi.org/10.48550/arxiv.1712.09990	text	January 2017
All-loop Mondrian Diagrammatics and 4-particle Amplituhedron An, Yang; Li, Yi; Li, Zhinan arXiv https://doi.org/10.48550/arxiv.1712.09994	text	January 2017
The Double Pentaladder Integral to All Orders Caron-Huot, Simon; Dixon, Lance J.; von Hippel, Matt arXiv https://doi.org/10.48550/arxiv.1806.01361	text	January 2018
All-loop cuts from the Amplituhedron Langer, Cameron; Srikant, Akshay Yelleshpur arXiv https://doi.org/10.48550/arxiv.1902.05951	text	January 2019
The Sklyanin Bracket and Cluster Adjacency at All Multiplicity Golden, John; McLeod, Andrew J.; Spradlin, Marcus arXiv https://doi.org/10.48550/arxiv.1902.11286	text	January 2019

Similar Records

The Amplituhedron

Journal Article · Mon Oct 06 00:00:00 EDT 2014 · Journal of High Energy Physics (Online) · OSTI ID:1598502

Arkani-Hamed, Nima; Trnka, Jaroslav

Anatomy of the amplituhedron

Journal Article · Tue Mar 24 00:00:00 EDT 2015 · Journal of High Energy Physics (Online) · OSTI ID:1598502

Franco, Sebastián; Galloni, Daniele; Mariotti, Alberto; +1 more

All-loop cuts from the Amplituhedron

Journal Article · Mon Apr 15 00:00:00 EDT 2019 · Journal of High Energy Physics (Online) · OSTI ID:1598502

Langer, Cameron; Srikant, Akshay Yelleshpur

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
supersymmetry: 4
geometry
scattering
unitarity
supersymmetric gauge theory
scattering amplitudes

Title: Into the amplituhedron

Citation Formats

References (12)

Cited By (31)

Similar Records

Related Subjects