- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access
  • Access by Xinjiang University

Collinear bootstrap for N =(1, 1) SYM theory

A. V. Belitsky1 and V. A. Smirnov2,3

  • 1Department of Physics, Arizona State University, Tempe, Arizona 85287-1504, USA
  • 2Skobeltsyn Institute of Nuclear Physics, Moscow State University, 119992 Moscow, Russia
  • 3Moscow Center for Fundamental and Applied Mathematics, 119992 Moscow, Russia

PDF

Phys. Rev. D 112, 105018 – Published 24 November, 2025

DOI: https://doi.org/10.1103/rt29-3dsm

Abstract

We study the multicollinear behavior of tree amplitudes in the six-dimensional N=(1,1) super Yang-Mills theory (sYM). A generalized dimensional reduction of the latter yields the four-dimensional N=4 sYM on the Coulomb branch, which is of interest for considerations of massive or off-shell scattering. To this end, we revisit the calculation of tree scattering in the former theory employing the collinear bootstrap and known massless limits. Assuming the universality of the double-collinear asymptotics, the result for six-leg superamplitudes differs from the one available in the literature. We further extract the triple-collinear splitting superamplitudes from these.

View figure in article

Physics Subject Headings (PhySH)

Corrections

1 December, 2025

Correction: An affiliation for the second author was missing at publication and has been inserted. The last sentence of the Acknowledgments section was incorrect and has been fixed.

Article Text

References (22)

  1. S. J. Parke and T. R. Taylor, An amplitude for n gluon scattering, Phys. Rev. Lett. 56, 2459 (1986).
  2. F. A. Berends and W. T. Giele, Recursive calculations for processes with n gluons, Nucl. Phys. B306, 759 (1988).
  3. M. L. Mangano and S. J. Parke, Multiparton amplitudes in gauge theories, Phys. Rep. 200, 301 (1991).
  4. S. Catani, D. de Florian, and G. Rodrigo, Space-like (versus time-like) collinear limits in QCD: Is factorization violated?, J. High Energy Phys. 07 (2012) 026.
  5. T. Dennen, Y.-t. Huang, and W. Siegel, Supertwistor space for 6D maximal super Yang-Mills, J. High Energy Phys. 04 (2010) 127.
  6. C. Cheung and D. O’Connell, Amplitudes and spinor-helicity in six dimensions, J. High Energy Phys. 07 (2009) 075.
  7. Z. Bern, J. J. Carrasco, T. Dennen, Y. T. Huang, and H. Ita, Generalized unitarity and six-dimensional helicity, Phys. Rev. D 83, 085022 (2011).
  8. T. Dennen and Y.-t. Huang, Dual conformal properties of six-dimensional maximal super Yang-Mills amplitudes, J. High Energy Phys. 01 (2011) 140.
  9. Y.-t. Huang, Non-chiral s-matrix of N=4 super Yang-Mills, arXiv:1104.2021.
  10. J. Plefka, T. Schuster, and V. Verschinin, From six to four and more: Massless and massive maximal super Yang-Mills amplitudes in 6D and 4D and their hidden symmetries, J. High Energy Phys. 01 (2015) 098.
  11. R. Britto, F. Cachazo, and B. Feng, New recursion relations for tree amplitudes of gluons, Nucl. Phys. B715, 499 (2005).
  12. R. Britto, F. Cachazo, B. Feng, and E. Witten, Direct proof of tree-level recursion relation in Yang-Mills theory, Phys. Rev. Lett. 94, 181602 (2005).
  13. A. V. Belitsky, Collinear anatomy, J. High Energy Phys. 05 (2025) 117.
  14. G. P. Korchemsky and E. Sokatchev, Symmetries and analytic properties of scattering amplitudes in N=4 SYM theory, Nucl. Phys. B832, 1 (2010).
  15. J. M. Drummond, J. Henn, G. P. Korchemsky, and E. Sokatchev, Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory, Nucl. Phys. B828, 317 (2010).
  16. O. Steinmann, Ueber den Zusammenhang zwischen den Wightmanfunktionen und den retardierten Kommutatoren, Ph.D. thesis, ETH Zürich, 1960, 10.3929/ethz-a-000107369..
  17. S. Caron-Huot, L. J. Dixon, A. McLeod, and M. von Hippel, Bootstrapping a five-loop amplitude using Steinmann relations, Phys. Rev. Lett. 117, 241601 (2016).
  18. R. Mertig, M. Bohm, and A. Denner, feyncalc: Computer algebraic calculation of Feynman amplitudes, Comput. Phys. Commun. 64, 345 (1991).
  19. V. Shtabovenko, R. Mertig, and F. Orellana, feyncalc 10: Do multiloop integrals dream of computer codes?, Comput. Phys. Commun. 306, 109357 (2025).
  20. Z. Bern, L. J. Dixon, D. C. Dunbar, and D. A. Kosower, One loop n point gauge theory amplitudes, unitarity and collinear limits, Nucl. Phys. B425, 217 (1994).
  21. Z. Bern, L. J. Dixon, D. C. Dunbar, and D. A. Kosower, Fusing gauge theory tree amplitudes into loop amplitudes, Nucl. Phys. B435, 59 (1995).
  22. Z. Bern, L. J. Dixon, and D. A. Kosower, Two-loop g→gg splitting amplitudes in QCD, J. High Energy Phys. 08 (2004) 012.

Outline

Information

Phys. Rev. D 112, 105018– Published 24 November, 2025
  • Received 27 August 2025
  • Accepted 10 November 2025
  • Corrected 1 December 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation