Abstract
We write down closed formulas for all necessary steps to obtain multiparticle super Yang-Mills superfields in the so-called BCJ gauge. The superfields in this gauge have obvious applications in the quest for finding BCJ-satisfying representations of amplitudes. As a benefit of having these closed formulas, we identify the explicit finite gauge transformation responsible for attaining the BCJ gauge. To do this, several combinatorial maps on words are introduced and associated identities rigorously proven.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
C.R. Mafra and O. Schlotterer, Multiparticle SYM equations of motion and pure spinor BRST blocks, JHEP07 (2014) 153 [arXiv:1404.4986] [INSPIRE].
S. Lee, C.R. Mafra and O. Schlotterer, Non-linear gauge transformations in D = 10 SYM theory and the BCJ duality, JHEP03 (2016) 090 [arXiv:1510.08843] [INSPIRE].
L. Brink, J.H. Schwarz and J. Scherk, Supersymmetric Yang-Mills Theories, Nucl. Phys. B 121 (1977) 77 [INSPIRE].
C.R. Mafra, O. Schlotterer and S. Stieberger, Complete N-Point Superstring Disk Amplitude I. Pure Spinor Computation, Nucl. Phys. B 873 (2013) 419 [arXiv:1106.2645] [INSPIRE].
C.R. Mafra, O. Schlotterer, S. Stieberger and D. Tsimpis, A recursive method for SYM n-point tree amplitudes, Phys. Rev. D 83 (2011) 126012 [arXiv:1012.3981] [INSPIRE].
N. Berkovits, Super Poincaré covariant quantization of the superstring, JHEP04 (2000) 018 [hep-th/0001035] [INSPIRE].
N. Berkovits, ICTP lectures on covariant quantization of the superstring, ICTP Lect. Notes Ser. 13 (2003) 57 [hep-th/0209059] [INSPIRE].
C.R. Mafra and O. Schlotterer, Berends-Giele recursions and the BCJ duality in superspace and components, JHEP03 (2016) 097 [arXiv:1510.08846] [INSPIRE].
F.A. Berends and W.T. Giele, Recursive Calculations for Processes with n Gluons, Nucl. Phys. B 306 (1988) 759 [INSPIRE].
D. Blessenohl and H. Laue, Generalized Jacobi identities, Note Mat.8 (1988) 111.
Z. Bern, J.J.M. Carrasco and H. Johansson, New Relations for Gauge-Theory Amplitudes, Phys. Rev. D 78 (2008) 085011 [arXiv:0805.3993] [INSPIRE].
Z. Bern, J.J.M. Carrasco and H. Johansson, Perturbative Quantum Gravity as a Double Copy of Gauge Theory, Phys. Rev. Lett. 105 (2010) 061602 [arXiv:1004.0476] [INSPIRE].
C.R. Mafra, O. Schlotterer and S. Stieberger, Explicit BCJ Numerators from Pure Spinors, JHEP07 (2011) 092 [arXiv:1104.5224] [INSPIRE].
C.R. Mafra and O. Schlotterer, Towards one-loop SYM amplitudes from the pure spinor BRST cohomology, Fortsch. Phys. 63 (2015) 105 [arXiv:1410.0668] [INSPIRE].
C.R. Mafra and O. Schlotterer, Two-loop five-point amplitudes of super Yang-Mills and supergravity in pure spinor superspace, JHEP10 (2015) 124 [arXiv:1505.02746] [INSPIRE].
K.G. Selivanov, On tree form-factors in (supersymmetric) Yang-Mills theory, Commun. Math. Phys.208 (2000) 671 [hep-th/9809046] [INSPIRE].
K.G. Selivanov, Post-classicism in Tree Amplitudes, in Proceedings of 34th Rencontres de Moriond on Electroweak Interactions and Unified Theories, Les Arcs France (1999), pg. 473 [hep-th/9905128] [INSPIRE].
E. Witten, Twistor-Like Transform in Ten-Dimensions, Nucl. Phys. B 266 (1986) 245 [INSPIRE].
W. Siegel, Superfields in Higher Dimensional Space-time, Phys. Lett. B 80 (1979) 220 [INSPIRE].
C. Reutenauer, Free Lie Algebras, London Mathematical Society Monographs, Clarendon Press, Oxford U.K. (1993).
C.R. Mafra and O. Schlotterer, Towards the n-point one-loop superstring amplitude. Part I. Pure spinors and superfield kinematics, JHEP08 (2019) 090 [arXiv:1812.10969] [INSPIRE].
J.-Y. Thibon, Lie idempotents in descent algebras, (lecture notes), Workshop on Hopf Algebras and Props, Boston U.S.A. (2007).
H. Barcelo and S. Sundaram, On Some Submodules of the Action of the Symmetrical Group on the Free Lie Algebra, J. Algebra154 (1993) 12.
J.A.M. Vermaseren, New features of FORM, math-ph/0010025 [INSPIRE].
M. Tentyukov and J.A.M. Vermaseren, The Multithreaded version of FORM, Comput. Phys. Commun. 181 (2010) 1419 [hep-ph/0702279][INSPIRE].
N. Berkovits, Explaining Pure Spinor Superspace, hep-th/0612021 [INSPIRE].
N. Berkovits, Untwisting the pure spinor formalism to the RNS and twistor string in a flat and AdS5× S5background, JHEP06 (2016) 127 [arXiv:1604.04617] [INSPIRE].
L.M. Garozzo, L. Queimada and O. Schlotterer, Berends-Giele currents in Bern-Carrasco-Johansson gauge for F3- and F4-deformed Yang-Mills amplitudes, JHEP02 (2019) 078 [arXiv:1809.08103] [INSPIRE].
R. Monteiro and D. O’Connell, The Kinematic Algebra From the Self-Dual Sector, JHEP07 (2011) 007 [arXiv:1105.2565] [INSPIRE].
G. Chen, H. Johansson, F. Teng and T. Wang, On the kinematic algebra for BCJ numerators beyond the MHV sector, arXiv:1906.10683 [INSPIRE].
T. Macrelli, C. Sämann and M. Wolf, Scattering amplitude recursion relations in Batalin-Vilkovisky-quantizable theories, Phys. Rev.D 100 (2019) 045017 [arXiv:1903.05713] [INSPIRE].
F.A. Berends and W.T. Giele, Multiple Soft Gluon Radiation in Parton Processes, Nucl. Phys. B 313 (1989) 595 [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: 1906.12252
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, 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 licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Bridges, E., Mafra, C.R. Algorithmic construction of SYM multiparticle superfields in the BCJ gauge. J. High Energ. Phys. 2019, 22 (2019). https://doi.org/10.1007/JHEP10(2019)022
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2019)022