Abstract
In this note we investigate Graßmannian formulas for form factors of the chiral part of the stress-tensor multiplet in \( \mathcal{N}=4 \) superconformal Yang-Mills theory. We present an all-n contour for the G(3, n + 2) Graßmannian integral of NMHV form factors derived from on-shell 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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
E. Witten, Perturbative gauge theory as a string theory in twistor space, Commun. Math. Phys. 252 (2004) 189 [hep-th/0312171] [INSPIRE].
N. Beisert et al., Review of AdS/CFT integrability: an overview, Lett. Math. Phys. 99 (2012) 3 [arXiv:1012.3982] [INSPIRE].
J.M. Drummond, J.M. Henn and J. Plefka, Yangian symmetry of scattering amplitudes in N = 4 super Yang-Mills theory, JHEP 05 (2009) 046 [arXiv:0902.2987] [INSPIRE].
L. Ferro, T. Lukowski, C. Meneghelli, J. Plefka and M. Staudacher, Spectral parameters for scattering amplitudes in N = 4 super Yang-Mills theory, JHEP 01 (2014) 094 [arXiv:1308.3494] [INSPIRE].
D. Chicherin, S. Derkachov and R. Kirschner, Yang-Baxter operators and scattering amplitudes in N = 4 super-Yang-Mills theory, Nucl. Phys. B 881 (2014) 467 [arXiv:1309.5748] [INSPIRE].
N. Arkani-Hamed, F. Cachazo, C. Cheung and J. Kaplan, A duality for the S matrix, JHEP 03 (2010) 020 [arXiv:0907.5418] [INSPIRE].
N. Arkani-Hamed et al., Scattering Amplitudes and the Positive Grassmannian, Cambridge University Press, Cambridge U.K. (2012), arXiv:1212.5605.
B. Eden, P. Heslop and L. Mason, The correlahedron, arXiv:1701.00453 [INSPIRE].
N. Arkani-Hamed and J. Trnka, The amplituhedron, JHEP 10 (2014) 030 [arXiv:1312.2007] [INSPIRE].
N. Arkani-Hamed and J. Trnka, Into the amplituhedron, JHEP 12 (2014) 182 [arXiv:1312.7878] [INSPIRE].
A. Brandhuber, B. Spence, G. Travaglini and G. Yang, Form factors in N = 4 super Yang-Mills and periodic Wilson loops, JHEP 01 (2011) 134 [arXiv:1011.1899] [INSPIRE].
A. Brandhuber, O. Gurdogan, R. Mooney, G. Travaglini and G. Yang, Harmony of super form factors, JHEP 10 (2011) 046 [arXiv:1107.5067] [INSPIRE].
L.V. Bork, On NMHV form factors in N = 4 SYM theory from generalized unitarity, JHEP 01 (2013) 049 [arXiv:1203.2596] [INSPIRE].
L.V. Bork, On form factors in \( \mathcal{N}=4 \) SYM theory and polytopes, JHEP 12 (2014) 111 [arXiv:1407.5568] [INSPIRE].
L.V. Bork and A.I. Onishchenko, Grassmannians and form factors with q 2 = 0 in \( \mathcal{N}=4 \) SYM theory, JHEP 12 (2016) 076 [arXiv:1607.00503] [INSPIRE].
L.V. Bork and A.I. Onishchenko, Form factors in the \( \mathcal{N}=4 \) maximally supersymmetric Yang-Mills theory, soft theorems, and integrability, Theor. Math. Phys. 190 (2017) 335.
B. Eden, P. Heslop, G.P. Korchemsky and E. Sokatchev, The super-correlator/super-amplitude duality: part I, Nucl. Phys. B 869 (2013) 329 [arXiv:1103.3714] [INSPIRE].
B. Eden, P. Heslop, G.P. Korchemsky and E. Sokatchev, The super-correlator/super-amplitude duality: part II, Nucl. Phys. B 869 (2013) 378 [arXiv:1103.4353] [INSPIRE].
R. Frassek, D. Meidinger, D. Nandan and M. Wilhelm, On-shell diagrams, Graßmannians and integrability for form factors, JHEP 01 (2016) 182 [arXiv:1506.08192] [INSPIRE].
R. Britto, F. Cachazo, B. Feng and E. Witten, Direct proof of tree-level recursion relation in Yang-Mills theory, Phys. Rev. Lett. 94 (2005) 181602 [hep-th/0501052] [INSPIRE].
J.A. Farrow and A.E. Lipstein, From 4D ambitwistor strings to on shell diagrams and back, JHEP 07 (2017) 114 [arXiv:1705.07087] [INSPIRE].
M. Spradlin and A. Volovich, From twistor string theory to recursion relations, Phys. Rev. D 80 (2009) 085022 [arXiv:0909.0229] [INSPIRE].
L. Dolan and P. Goddard, Gluon tree amplitudes in open twistor string theory, JHEP 12 (2009) 032 [arXiv:0909.0499] [INSPIRE].
R. Roiban, M. Spradlin and A. Volovich, On the tree level S matrix of Yang-Mills theory, Phys. Rev. D 70 (2004) 026009 [hep-th/0403190] [INSPIRE].
N. Arkani-Hamed, F. Cachazo, C. Cheung and J. Kaplan, The S-matrix in twistor space, JHEP 03 (2010) 110 [arXiv:0903.2110] [INSPIRE].
D. Nandan, A. Volovich and C. Wen, A Grassmannian etude in NMHV minors, JHEP 07 (2010) 061 [arXiv:0912.3705] [INSPIRE].
N. Arkani-Hamed, J. Bourjaily, F. Cachazo and J. Trnka, Unification of residues and Grassmannian dualities, JHEP 01 (2011) 049 [arXiv:0912.4912] [INSPIRE].
J.L. Bourjaily, J. Trnka, A. Volovich and C. Wen, The Grassmannian and the twistor string: connecting all trees in N = 4 SYM, JHEP 01 (2011) 038 [arXiv:1006.1899] [INSPIRE].
A. Brandhuber, E. Hughes, R. Panerai, B. Spence and G. Travaglini, The connected prescription for form factors in twistor space, JHEP 11 (2016) 143 [arXiv:1608.03277] [INSPIRE].
S. He and Z. Liu, A note on connected formula for form factors, JHEP 12 (2016) 006 [arXiv:1608.04306] [INSPIRE].
S. Franco, D. Galloni, B. Penante and C. Wen, Non-planar on-shell diagrams, JHEP 06 (2015) 199 [arXiv:1502.02034] [INSPIRE].
J.L. Bourjaily, S. Franco, D. Galloni and C. Wen, Stratifying on-shell cluster varieties: the geometry of non-planar on-shell diagrams, JHEP 10 (2016) 003 [arXiv:1607.01781] [INSPIRE].
L.V. Bork and A.I. Onishchenko, Four dimensional ambitwistor strings and form factors of local and Wilson line operators, arXiv:1704.04758 [INSPIRE].
H.S. White, Seven points on a twisted cubic curve, Proc. Natl. Acad. Sci. 1 (1915) 464.
D. Nandan and C. Wen, Generating all tree amplitudes in N = 4 SYM by inverse soft limit, JHEP 08 (2012) 040 [arXiv:1204.4841] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1707.00443
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Meidinger, D., Nandan, D., Penante, B. et al. A note on NMHV form factors from the Graßmannian and the twistor string. J. High Energ. Phys. 2017, 24 (2017). https://doi.org/10.1007/JHEP09(2017)024
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2017)024