Abstract
Inspired by the new soft theorem in gravity by Cachazo and Strominger, the soft theorem for color-ordered Yang-Mills amplitudes has also been identified by Casali. In this note, the same content of \( \mathcal{N} \) = 4 SYM using the Grassmannian formulation is studied. Explicitly, in the holomorphic soft limit, we reduce the n-particle amplitude in terms of Grassmannian contour integrations into the deformed (n − 1)-particle amplitude by localizing k variables relevant to the n-th particle. Afterwards, the leading soft factor and sub-leading soft operator naturally emerge.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
F.E. Low, Scattering of light of very low frequency by systems of spin 1/2, Phys. Rev. 96 (1954) 1428 [INSPIRE].
M. Gell-Mann and M.L. Goldberger, Scattering of low-energy photons by particles of spin 1/2, Phys. Rev. 96 (1954) 1433 [INSPIRE].
S. Saito, Low-energy theorem for Compton scattering, Phys. Rev. 184 (1969) 1894 [INSPIRE].
F.E. Low, Bremsstrahlung of very low-energy quanta in elementary particle collisions, Phys. Rev. 110 (1958) 974 [INSPIRE].
S. Weinberg, Photons and Gravitons in S-Matrix Theory: Derivation of Charge Conservation and Equality of Gravitational and Inertial Mass, Phys. Rev. 135 (1964) B1049 [INSPIRE].
S. Weinberg, Infrared Photons and Gravitons, Phys. Rev. 140 (1965) B516 [INSPIRE].
F. Cachazo and A. Strominger, Evidence for a New Soft Graviton Theorem, arXiv:1404.4091 [INSPIRE].
E. Casali, Soft sub-leading divergences in Yang-Mills amplitudes, JHEP 08 (2014) 077 [arXiv:1404.5551] [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, J. Bourjaily, F. Cachazo and J. Trnka, Unification of Residues and Grassmannian Dualities, JHEP 01 (2011) 049 [arXiv:0912.4912] [INSPIRE].
D. Nandan, A. Volovich and C. Wen, A Grassmannian Etude in NMHV Minors, JHEP 07 (2010) 061 [arXiv:0912.3705] [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].
Z.-W. Liu, Soft theorems in maximally supersymmetric theories, arXiv:1410.1616 [INSPIRE].
J. Broedel, M. de Leeuw, J. Plefka and M. Rosso, Constraining subleading soft gluon and graviton theorems, Phys. Rev. D 90 (2014) 065024 [arXiv:1406.6574] [INSPIRE].
Z. Bern, S. Davies, P. Di Vecchia and J. Nohle, Low-Energy Behavior of Gluons and Gravitons from Gauge Invariance, Phys. Rev. D 90 (2014) 084035 [arXiv:1406.6987] [INSPIRE].
C.D. White, Diagrammatic insights into next-to-soft corrections, Phys. Lett. B 737 (2014) 216 [arXiv:1406.7184] [INSPIRE].
A.J. Larkoski, Conformal Invariance of the Subleading Soft Theorem in Gauge Theory, Phys. Rev. D 90 (2014) 087701 [arXiv:1405.2346] [INSPIRE].
B.U.W. Schwab and A. Volovich, Subleading Soft Theorem in Arbitrary Dimensions from Scattering Equations, Phys. Rev. Lett. 113 (2014) 101601 [arXiv:1404.7749] [INSPIRE].
N. Afkhami-Jeddi, Soft Graviton Theorem in Arbitrary Dimensions, arXiv:1405.3533 [INSPIRE].
M. Zlotnikov, Sub-sub-leading soft-graviton theorem in arbitrary dimension, JHEP 10 (2014) 148 [arXiv:1407.5936] [INSPIRE].
C. Kalousios and F. Rojas, Next to subleading soft-graviton theorem in arbitrary dimensions, JHEP 01 (2015) 107 [arXiv:1407.5982] [INSPIRE].
Z. Bern, S. Davies and J. Nohle, On Loop Corrections to Subleading Soft Behavior of Gluons and Gravitons, Phys. Rev. D 90 (2014) 085015 [arXiv:1405.1015] [INSPIRE].
S. He, Y.-t. Huang and C. Wen, Loop Corrections to Soft Theorems in Gauge Theories and Gravity, JHEP 12 (2014) 115 [arXiv:1405.1410] [INSPIRE].
F. Cachazo and E.Y. Yuan, Are Soft Theorems Renormalized?, arXiv:1405.3413 [INSPIRE].
B.U.W. Schwab, Subleading Soft Factor for String Disk Amplitudes, JHEP 08 (2014) 062 [arXiv:1406.4172] [INSPIRE].
M. Bianchi, S. He, Y.-t. Huang and C. Wen, More on Soft Theorems: Trees, Loops and Strings, arXiv:1406.5155 [INSPIRE].
T. Adamo, E. Casali and D. Skinner, Perturbative gravity at null infinity, Class. Quant. Grav. 31 (2014) 225008 [arXiv:1405.5122] [INSPIRE].
Y. Geyer, A.E. Lipstein and L. Mason, Ambitwistor strings at null infinity and (subleading) soft limits, Class. Quant. Grav. 32 (2015) 055003 [arXiv:1406.1462] [INSPIRE].
Y.-J. Du, B. Feng, C.-H. Fu and Y. Wang, Note on Soft Graviton theorem by KLT Relation, JHEP 11 (2014) 090 [arXiv:1408.4179] [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: 1410.5047
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
Rao, J. Soft theorem of \( \mathcal{N} \) = 4 SYM in Grassmannian formulation. J. High Energ. Phys. 2015, 87 (2015). https://doi.org/10.1007/JHEP02(2015)087
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2015)087