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Grassmannians for scattering amplitudes in 4d $\mathcal{N}=4$ SYM and 3d ABJM

Authors
Henriette Elvang,YU-TIN HUANG
Cynthia Keeler,Thomas Lam,Timothy M. Olson,Samuel B. Roland,David E. Speyer,Joaquín Martínez-Sánchez,Vicente Mercado,Павел Зотов,Jan Nowak,Siobain Duffy,Chimit Ochirov,Vadim Kapuller,Gennady Novik,Yaroslav Kuzmin,Игорь Бакин,shona mackie,Айдар Султанов,Elena Suleymanova,Aleksandra Kotlova,Ibrahim Shehatta,Hsin-Yi Chao,Peter Kraal,Дамир Валишин,Svetlana Egorova,Nataliia Borys,João Faria,Maria Gabriela Basto de Lima,Donald Howarth,Zeki Yumuk,Светлана Смагина,Boris Revich,Evgeni Skryabin,YASUHIRO HARADA,Stepan Epoyan,Kirk Jensen,Philippa Brock,Lyudmila Patrina,Halyna Voznyak,Елена Мошненко,Sergey Zelentsov,N/A ,Pei-Ting Chuang,David Meeker,Galina Deryabina,margarida moura fernandes,Gyeong Hun ,Alexandru Ciubotaru,Carolyn Dzierba,Andrew Degnan,Andy Van Brocklin,Joseph Fotsing,Dragomir Bondžić,Thorsten Alexander Kern,marzia govoni,Kam Moon Lester LIU,HSIEN-HAO LIAO,Vladimir Shats,Chebolu Lakshmana Rao,Ольга Постнова,Steven Janowiecki,Nathaniel Butlin,Régis Sabbadin,Олександр Трухачов,Josef Káňa,Javier Martin-Garcia,Tatsuhiro Misumi,Arnthor Ævarsson,Min Andel,Chaitali Sengupta,MEEI-MEI CHEN,Lydia Philpott,Nicholas Demarais,Viktoriia Vapnichna,Monika Blanke,Fulai Guo,Ralph Pudritz,Bruce Balick,Yuri Chugaev,Andrey Tsvetkov,Igor Cherniaev,Khee-Gan Lee,Anna Cibinel,Jakobus le Roux,Ximena Fernández,HENNADII HAPICH,Pierre Frendo,Matthew Reece,Vladimir Kovalev,Stephen E Ryan,Richard Jefferson,Rupal Deva,Blaise Goutéraux,Mikhail Alfimov,Loay Ismail,Daniel Toboła,Alan Bakalinsky,Ahmed Maarouf,Filippo Sala,Miguel José Ruiz-Gómez,Shwu-yann Su ,Yuriy Arabadgi,Laura Puyol,Andre Catic,Hendrik Feldmann,Natalia Pshenichcnaya,Светлана Ивановна Малявская,Jörg Helmschrot,Vasiliy V Kozlov,Yakov Yadgarov,Mark Howard,Юлия Мамырко,Сергей Подлесный,Aleksandr Bushnev,Margaret Lucas,Seyed Yaser Ayazi,Anna Zsigmond,Sven Bossuyt,Wolfram Fürbeth,Alma Biscevic,Olha Lazorko,Leif Backman,Chien-Chia Liu,Yanuandri Putrasari,Heiko Goelzer,Johannes N. Blumenberg,Wanching Chow,Mafura Uandykova,Stella Yi,Matteo Sgammini,Jeffrey Tiger,Zhao Chen,Armin Schmidt,Shih-Wei Sheu,Gohar Mkoyan,Nicholas Ralston,saffet erdoğan,CHAU-HWA CHI,Ashutosh Awasthi,yujun ,Ki Hyun Kim,Михаил Вениаминович Маслов,Anastasiia Ivanova,Валентина Псарева,Denezhkina Irina,M. 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MCTP-14-36
Grassmannians for scattering amplitudes
in 4d N = 4 SYM and 3d ABJM
Henriette Elvang1, Yu-tin Huang2, Cynthia Keeler1, Thomas Lam3,
Timothy M. Olson1, Samuel B. Roland1, David E Speyer3
1Michigan Center for Theoretical Physics & Randall Laboratory of Physics
Department of Physics,
University of Michigan, 450 Church St, Ann Arbor, MI 48109, USA
2Department of Physics and Astronomy,
National Taiwan University, Taipei 10617, Taiwan, ROC
3Department of Mathematics,
University of Michigan, 530 Church St, Ann Arbor, MI 48109, USA
elvang, keelerc, tfylam, timolson, rolandsa, speyer@umich.edu,
yutinyt@gmail.com
Abstract
Scattering amplitudes in 4d N = 4 super Yang-Mills theory (SYM) can be de-
scribed by Grassmannian contour integrals whose form depends on whether the exter-
nal data is encoded in momentum space, twistor space, or momentum twistor space.
After a pedagogical review, we present a new, streamlined proof of the equivalence of
the three integral formulations. A similar strategy allows us to derive a new Grass-
mannian integral for 3d N = 6 ABJM theory amplitudes in momentum twistor space:
it is a contour integral in an orthogonal Grassmannian with the novel property that
the internal metric depends on the external data. The result can be viewed as a
central step towards developing an amplituhedron formulation for ABJM amplitudes.
Various properties of Grassmannian integrals are examined, including boundary prop-
erties, pole structure, and a homological interpretation of the global residue theorems
for N = 4 SYM.
arXiv:1410.0621v1 [hep-th] 2 Oct 2014
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