Abstract
We present a proof of perturbative unitarity for planar \( \mathcal{N} \) = 4 SYM, following from the geometry of the amplituhedron. This proof is valid for amplitudes of arbitrary multiplicity n, loop order L and MHV degree k.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Z. Bern, J.J.M. Carrasco, L.J. Dixon, H. Johansson and R. Roiban, Manifest ultraviolet behavior for the three-loop four-point amplitude of N = 8 supergravity, Phys. Rev.D 78 (2008) 105019 [arXiv:0808.4112] [INSPIRE].
C. Anastasiou, R. Britto, B. Feng, Z. Kunszt and P. Mastrolia, D-dimensional unitarity cut method, Phys. Lett.B 645 (2007) 213 [hep-ph/0609191] [INSPIRE].
R. Britto, F. Cachazo and B. Feng, Generalized unitarity and one-loop amplitudes in N = 4 super-Yang-Mills, Nucl. Phys.D 725 (2005) 275 [hep-th/0412103] [INSPIRE].
Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, Fusing gauge theory tree amplitudes into loop amplitudes, Nucl. Phys.B 435 (1995) 59 [hep-ph/9409265] [INSPIRE].
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.B 425 (1994) 217 [hep-ph/9403226] [INSPIRE].
R. Britto, F. Cachazo and B. Feng, New recursion relations for tree amplitudes of gluons, Nucl. Phys.D 715 (2005) 499 [hep-th/0412308] [INSPIRE].
N. Arkani-Hamed, J.L. Bourjaily, F. Cachazo, S. Caron-Huot and J. Trnka, The all-loop integrand for scattering amplitudes in planar N = 4 SYM, JHEP01 (2011) 041 [arXiv:1008.2958] [INSPIRE].
N. Arkani-Hamed, J.L. Bourjaily, F. Cachazo, A.B. Goncharov, A. Postnikov and J. Trnka, Grassmannian geometry of scattering amplitudes, Cambridge University Press, Cambridge, U.K. (2016) [arXiv:1212.5605] [INSPIRE].
N. Arkani-Hamed and J. Trnka, The amplituhedron, JHEP10 (2014) 030 [arXiv:1312.2007] [INSPIRE].
N. Arkani-Hamed and J. Trnka, Into the amplituhedron, JHEP12 (2014) 182 [arXiv:1312.7878] [INSPIRE].
A. Hodges, Eliminating spurious poles from gauge-theoretic amplitudes, JHEP05 (2013) 135 [arXiv:0905.1473] [INSPIRE].
N. Arkani-Hamed, J.L. Bourjaily, F. Cachazo, A. Hodges and J. Trnka, A note on polytopes for scattering amplitudes, JHEP04 (2012) 081 [arXiv:1012.6030] [INSPIRE].
N. Arkani-Hamed, F. Cachazo, C. Cheung and J. Kaplan, A duality for the S matrix, JHEP03 (2010) 020 [arXiv:0907.5418] [INSPIRE].
L.J. Mason and D. Skinner, Dual superconformal invariance, momentum twistors and Grassmannians, JHEP11 (2009) 045 [arXiv:0909.0250] [INSPIRE].
A. Postnikov, Total positivity, Grassmannians and networks, math.CO/0609764 [INSPIRE].
N. Arkani-Hamed, H. Thomas and J. Trnka, Unwinding the amplituhedron in binary, JHEP01 (2018) 016 [arXiv:1704.05069] [INSPIRE].
J.L. Bourjaily, J. Trnka, A. Volovich and C. Wen, The Grassmannian and the twistor string: connecting all trees in N = 4 SYM, JHEP01 (2011) 038 [arXiv:1006.1899] [INSPIRE].
N. Arkani-Hamed, F. Cachazo and C. Cheung, The Grassmannian origin of dual superconformal invariance, JHEP03 (2010) 036 [arXiv:0909.0483] [INSPIRE].
N. Arkani-Hamed, J.L. Bourjaily, F. Cachazo and J. Trnka, Local integrals for planar scattering amplitudes, JHEP06 (2012) 125 [arXiv:1012.6032] [INSPIRE].
C. Langer and A. Yelleshpur Srikant, All-loop cuts from the amplituhedron, JHEP04 (2019) 105 [arXiv:1902.05951] [INSPIRE].
N. Arkani-Hamed, C. Langer, A. Yelleshpur Srikant and J. Trnka, Deep into the amplituhedron: amplitude singularities at all loops and legs, Phys. Rev. Lett.122 (2019) 051601 [arXiv:1810.08208] [INSPIRE].
S. Caron-Huot, Loops and trees, JHEP05 (2011) 080 [arXiv:1007.3224] [INSPIRE].
N. Arkani-Hamed, Y. Bai and T. Lam, Positive geometries and canonical forms, JHEP11 (2017) 039 [arXiv:1703.04541] [INSPIRE].
G. Salvatori, 1-loop amplitudes from the halohedron, JHEP12 (2019) 074 [arXiv:1806.01842] [INSPIRE].
G. Salvatori and S.L. Cacciatori, Hyperbolic geometry and amplituhedra in 1 + 2 dimensions, JHEP08 (2018) 167 [arXiv:1803.05809] [INSPIRE].
S. He, G. Yan, C. Zhang and Y. Zhang, Scattering forms, worldsheet forms and amplitudes from subspaces, JHEP08 (2018) 040 [arXiv:1803.11302] [INSPIRE].
N. Arkani-Hamed, Y. Bai, S. He and G. Yan, Scattering forms and the positive geometry of kinematics, color and the worldsheet, JHEP05 (2018) 096 [arXiv:1711.09102] [INSPIRE].
S. He and C. Zhang, Notes on scattering amplitudes as differential forms, JHEP10 (2018) 054 [arXiv:1807.11051] [INSPIRE].
D. Damgaard, L. Ferro, T. Lukowski and M. Parisi, The momentum amplituhedron, JHEP08 (2019) 042 [arXiv:1905.04216] [INSPIRE].
C. Anastasiou, R. Britto, B. Feng, Z. Kunszt and P. Mastrolia, Unitarity cuts and reduction to master integrals in d dimensions for one-loop amplitudes, JHEP03 (2007) 111 [hep-ph/0612277] [INSPIRE].
R.E. Cutkosky, Singularities and discontinuities of Feynman amplitudes, J. Math. Phys.1 (1960) 429 [INSPIRE].
R.J. Eden, P.V. Landshoff, D.I. Olive and J.C. Polkinghorne, The analytic S-matrix. Cambridge Univ. Press, Cambridge, U.K. (1966) [INSPIRE].
T. Lukowski, On the boundaries of the m = 2 amplituhedron, arXiv:1908.00386 [INSPIRE].
S. Franco, D. Galloni, A. Mariotti and J. Trnka, Anatomy of the amplituhedron, JHEP03 (2015) 128 [arXiv:1408.3410] [INSPIRE].
D. Galloni, Positivity sectors and the amplituhedron, arXiv:1601.02639 [INSPIRE].
I. Prlina, M. Spradlin, J. Stankowicz and S. Stanojevic, Boundaries of amplituhedra and NMHV symbol alphabets at two loops, JHEP04 (2018) 049 [arXiv:1712.08049] [INSPIRE].
I. Prlina, M. Spradlin, J. Stankowicz, S. Stanojevic and A. Volovich, All-helicity symbol alphabets from unwound amplituhedra, JHEP05 (2018) 159 [arXiv:1711.11507] [INSPIRE].
T. Dennen, I. Prlina, M. Spradlin, S. Stanojevic and A. Volovich, Landau singularities from the amplituhedron, JHEP06 (2017) 152 [arXiv:1612.02708] [INSPIRE].
T. Dennen, M. Spradlin and A. Volovich, Landau singularities and symbology: one- and two-loop MHV amplitudes in SYM theory, JHEP03 (2016) 069 [arXiv:1512.07909] [INSPIRE].
I. Prlina, M. Spradlin and S. Stanojevic, All-loop singularities of scattering amplitudes in massless planar theories, Phys. Rev. Lett.121 (2018) 081601 [arXiv:1805.11617] [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: 1906.10700
Rights and permissions
This article is published under an open access license. Please check the 'Copyright Information' section either on this page or in the PDF for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.
About this article
Cite this article
Srikant, A.Y. Emergent unitarity from the amplituhedron. J. High Energ. Phys. 2020, 69 (2020). https://doi.org/10.1007/JHEP01(2020)069
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2020)069