A note on NMHV form factors from the Graßmannian and the twistor string
Abstract
In this note we investigate Graßmannian formulas for form factors of the chiral part of the stresstensor multiplet in N = 4 superconformal YangMills theory. We present an alln contour for the G(3, n + 2) Graßmannian integral of NMHV form factors derived from onshell diagrams and the BCFW recursion relation. In addition, we study other G(3, n + 2) formulas obtained from the connected prescription introduced recently. We find a recursive expression for all n and study its properties. For n ≥ 6, our formula has the same recursive structure as its amplitude counterpart, making its soft behaviour manifest. Finally, we explore the connection between the two Graßmannian formulations, using the global residue theorem, and find that it is much more intricate compared to scattering amplitudes.
 Authors:

 Humboldt Univ. of Berlin (Germany). Inst. of Mathematics. Inst. of Physics
 Univ. of Edinburgh, Scotland (United Kingdom). Higgs Centre for Theoretical Physics. School of Physics and Astronomy; Univ. of California, Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics
 European Organization for Nuclear Research (CERN), Geneva (Switzerland). Theory Division
 California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics; Univ. of California, Los Angeles, CA (United States). Mani L. Bhaumik Inst. for Theoretical Physics. Dept. of Physics and Astronomy; Univ. of California, Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics
 Publication Date:
 Research Org.:
 California Institute of Technology (CalTech), Pasadena, CA (United States); Univ. of Edinburgh, Scotland (United Kingdom)
 Sponsoring Org.:
 USDOE Office of Science (SC), High Energy Physics (HEP) (SC25); National Science Foundation (NSF); European Research Council (ERC); Science and Technology Facilities Council (STFC) (United Kingdom)
 OSTI Identifier:
 1424590
 Grant/Contract Number:
 SC0010255; PHY1125915; 637019
 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: 2017; Journal Issue: 9; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; duality in gauge field theories; scattering amplitudes; supersymmetric gauge theory
Citation Formats
Meidinger, David, Nandan, Dhritiman, Penante, Brenda, and Wen, Congkao. A note on NMHV form factors from the Graßmannian and the twistor string. United States: N. p., 2017.
Web. doi:10.1007/JHEP09(2017)024.
Meidinger, David, Nandan, Dhritiman, Penante, Brenda, & Wen, Congkao. A note on NMHV form factors from the Graßmannian and the twistor string. United States. doi:10.1007/JHEP09(2017)024.
Meidinger, David, Nandan, Dhritiman, Penante, Brenda, and Wen, Congkao. Wed .
"A note on NMHV form factors from the Graßmannian and the twistor string". United States. doi:10.1007/JHEP09(2017)024. https://www.osti.gov/servlets/purl/1424590.
@article{osti_1424590,
title = {A note on NMHV form factors from the Graßmannian and the twistor string},
author = {Meidinger, David and Nandan, Dhritiman and Penante, Brenda and Wen, Congkao},
abstractNote = {In this note we investigate Graßmannian formulas for form factors of the chiral part of the stresstensor multiplet in N = 4 superconformal YangMills theory. We present an alln contour for the G(3, n + 2) Graßmannian integral of NMHV form factors derived from onshell diagrams and the BCFW recursion relation. In addition, we study other G(3, n + 2) formulas obtained from the connected prescription introduced recently. We find a recursive expression for all n and study its properties. For n ≥ 6, our formula has the same recursive structure as its amplitude counterpart, making its soft behaviour manifest. Finally, we explore the connection between the two Graßmannian formulations, using the global residue theorem, and find that it is much more intricate compared to scattering amplitudes.},
doi = {10.1007/JHEP09(2017)024},
journal = {Journal of High Energy Physics (Online)},
number = 9,
volume = 2017,
place = {United States},
year = {2017},
month = {9}
}
Web of Science
Works referenced in this record:
On NMHV form factors in $ \mathcal{N}=4 $ SYM theory from generalized unitarity
journal, January 2013
 Bork, L. V.
 Journal of High Energy Physics, Vol. 2013, Issue 1
Perturbative Gauge Theory as a String Theory in Twistor Space
journal, October 2004
 Witten, Edward
 Communications in Mathematical Physics, Vol. 252, Issue 13
The Grassmannian and the twistor string: connecting all trees in $ \mathcal{N} = 4 $ SYM
journal, January 2011
 Bourjaily, Jacob L.; Trnka, Jaroslav; Volovich, Anastasia
 Journal of High Energy Physics, Vol. 2011, Issue 1
From twistor string theory to recursion relations
journal, October 2009
 Spradlin, Marcus; Volovich, Anastasia
 Physical Review D, Vol. 80, Issue 8
Yangian symmetry of scattering amplitudes in 𝒩 = 4 super YangMills theory
journal, May 2009
 Drummond, James; Henn, Johannes; Plefka, Jan
 Journal of High Energy Physics, Vol. 2009, Issue 05
From 4d ambitwistor strings to on shell diagrams and back
journal, July 2017
 Farrow, Joseph A.; Lipstein, Arthur E.
 Journal of High Energy Physics, Vol. 2017, Issue 7
The connected prescription for form factors in twistor space
journal, November 2016
 Brandhuber, A.; Hughes, E.; Panerai, R.
 Journal of High Energy Physics, Vol. 2016, Issue 11
The Amplituhedron
journal, October 2014
 ArkaniHamed, Nima; Trnka, Jaroslav
 Journal of High Energy Physics, Vol. 2014, Issue 10
Spectral parameters for scattering amplitudes in $ \mathcal{N} $ =4 super YangMills theory
journal, January 2014
 Ferro, Livia; Lukowski, Tomasz; Meneghelli, Carlo
 Journal of High Energy Physics, Vol. 2014, Issue 1
Onshell diagrams, Graßmannians and integrability for form factors
journal, January 2016
 Frassek, Rouven; Meidinger, David; Nandan, Dhritiman
 Journal of High Energy Physics, Vol. 2016, Issue 1
Grassmannians and form factors with q 2 = 0 in N $$ \mathcal{N} $$ =4 SYM theory
journal, December 2016
 Bork, L. V.; Onishchenko, A. I.
 Journal of High Energy Physics, Vol. 2016, Issue 12
Review of AdS/CFT Integrability: An Overview
journal, October 2011
 Beisert, Niklas; Ahn, Changrim; Alday, Luis F.
 Letters in Mathematical Physics, Vol. 99, Issue 13
A duality for the S matrix
journal, March 2010
 ArkaniHamed, N.; Cachazo, F.; Cheung, C.
 Journal of High Energy Physics, Vol. 2010, Issue 3
Gluon tree amplitudes in open twistor string theory
journal, December 2009
 Dolan, Louise; Goddard, Peter
 Journal of High Energy Physics, Vol. 2009, Issue 12
Form factors in the N=4 maximally supersymmetric Yang–Mills theory, soft theorems, and integrability
journal, March 2017
 Bork, L. V.; Onishchenko, A. I.
 Theoretical and Mathematical Physics, Vol. 190, Issue 3
Treelevel S matrix of YangMills theory
journal, July 2004
 Roiban, Radu; Spradlin, Marcus; Volovich, Anastasia
 Physical Review D, Vol. 70, Issue 2
Harmony of super form factors
journal, October 2011
 Brandhuber, A.; Gürdoğan, Ö.; Mooney, R.
 Journal of High Energy Physics, Vol. 2011, Issue 10
Stratifying onshell cluster varieties: the geometry of nonplanar onshell diagrams
journal, October 2016
 Bourjaily, Jacob L.; Franco, Sebastián; Galloni, Daniele
 Journal of High Energy Physics, Vol. 2016, Issue 10
Unification of residues and Grassmannian dualities
journal, January 2011
 ArkaniHamed, N.; Bourjaily, J.; Cachazo, F.
 Journal of High Energy Physics, Vol. 2011, Issue 1
Seven Points on a Twisted Cubic Curve
journal, August 1915
 White, H. S.
 Proceedings of the National Academy of Sciences, Vol. 1, Issue 8
Into the amplituhedron
journal, December 2014
 ArkaniHamed, Nima; Trnka, Jaroslav
 Journal of High Energy Physics, Vol. 2014, Issue 12
Generating all tree amplitudes in $ \mathcal{N} = 4\;{\text{SYM}} $ by Inverse Soft Limit
journal, August 2012
 Nandan, Dhritiman; Wen, Congkao
 Journal of High Energy Physics, Vol. 2012, Issue 8
The supercorrelator/superamplitude duality: Part II
journal, April 2013
 Eden, Burkhard; Heslop, Paul; Korchemsky, Gregory P.
 Nuclear Physics B, Vol. 869, Issue 3
The supercorrelator/superamplitude duality: Part I
journal, April 2013
 Eden, Burkhard; Heslop, Paul; Korchemsky, Gregory P.
 Nuclear Physics B, Vol. 869, Issue 3
The Smatrix in twistor space
journal, March 2010
 ArkaniHamed, N.; Cachazo, F.; Cheung, C.
 Journal of High Energy Physics, Vol. 2010, Issue 3
Nonplanar onshell diagrams
journal, June 2015
 Franco, Sebastián; Galloni, Daniele; Penante, Brenda
 Journal of High Energy Physics, Vol. 2015, Issue 6
Yang–Baxter operators and scattering amplitudes in <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchemainstance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/structbib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/structaff/dtd"><mml:mi mathvariant="script">N</mml:mi><mml:mo>=</mml:mo><mml:mn>4</mml:mn></mml:math> superYang–Mills theory
journal, April 2014
 Chicherin, D.; Derkachov, S.; Kirschner, R.
 Nuclear Physics B, Vol. 881
Form factors in $ \mathcal{N} = 4 $ super YangMills and periodic Wilson loops
journal, January 2011
 Brandhuber, Andreas; Spence, Bill; Travaglini, Gabriele
 Journal of High Energy Physics, Vol. 2011, Issue 1
Direct Proof of the TreeLevel Scattering Amplitude Recursion Relation in YangMills Theory
journal, May 2005
 Britto, Ruth; Cachazo, Freddy; Feng, Bo
 Physical Review Letters, Vol. 94, Issue 18
On form factors in N = 4 $$ \mathcal{N}=4 $$ SYM theory and polytopes
journal, December 2014
 Bork, L. V.
 Journal of High Energy Physics, Vol. 2014, Issue 12
A note on connected formula for form factors
journal, December 2016
 He, Song; Liu, Zhengwen
 Journal of High Energy Physics, Vol. 2016, Issue 12
A grassmannian étude in NMHV minors
journal, July 2010
 Nandan, Dhritiman; Volovich, Anastasia; Wen, Congkao
 Journal of High Energy Physics, Vol. 2010, Issue 7