Abstract
We extend the Operator Product Expansion (OPE) for scattering amplitudes in planar \( \mathcal{N}=4 \) SYM to account for all possible helicities of the external states. This is done by constructing a simple map between helicity configurations and so-called charged pentagon transitions. These OPE building blocks are generalizations of the bosonic pentagons entering MHV amplitudes and they can be bootstrapped at finite coupling from the integrable dynamics of the color flux tube. A byproduct of our map is a simple realization of parity in the super Wilson loop picture.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
B. Basso, A. Sever and P. Vieira, Spacetime and Flux Tube S-Matrices at Finite Coupling for N = 4 Supersymmetric Yang-Mills Theory, Phys. Rev. Lett. 111 (2013) 091602 [ar**v:1303.1396] [INSPIRE].
L.F. Alday, D. Gaiotto, J. Maldacena, A. Sever and P. Vieira, An Operator Product Expansion for Polygonal null Wilson Loops, JHEP 04 (2011) 088 [ar**v:1006.2788] [INSPIRE].
A. Sever and P. Vieira, Multichannel Conformal Blocks for Polygon Wilson Loops, JHEP 01 (2012) 070 [ar**v:1105.5748] [INSPIRE].
B. Basso, Exciting the GKP string at any coupling, Nucl. Phys. B 857 (2012) 254 [ar**v:1010.5237] [INSPIRE].
B. Basso, A. Sever and P. Vieira, Space-time S-matrix and Flux tube S-matrix II. Extracting and Matching Data, JHEP 01 (2014) 008 [ar**v:1306.2058] [INSPIRE].
B. Basso, A. Sever and P. Vieira, Space-time S-matrix and Flux-tube S-matrix III. The two-particle contributions, JHEP 08 (2014) 085 [ar**v:1402.3307] [INSPIRE].
B. Basso, A. Sever and P. Vieira, Space-time S-matrix and Flux-tube S-matrix IV. Gluons and Fusion, JHEP 09 (2014) 149 [ar**v:1407.1736] [INSPIRE].
B. Basso, J. Caetano, L. Cordova, A. Sever and P. Vieira, OPE for all Helicity Amplitudes II. Data analysis and Form Factors, to appear.
L.F. Alday and J.M. Maldacena, Gluon scattering amplitudes at strong coupling, JHEP 06 (2007) 064 [ar**v:0705.0303] [INSPIRE].
J.M. Drummond, G.P. Korchemsky and E. Sokatchev, Conformal properties of four-gluon planar amplitudes and Wilson loops, Nucl. Phys. B 795 (2008) 385 [ar**v:0707.0243] [INSPIRE].
A. Brandhuber, P. Heslop and G. Travaglini, MHV amplitudes in N = 4 super Yang-Mills and Wilson loops, Nucl. Phys. B 794 (2008) 231 [ar**v:0707.1153] [INSPIRE].
Z. Bern et al., The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory, Phys. Rev. D 78 (2008) 045007 [ar**v:0803.1465] [INSPIRE].
J.M. Drummond, J. Henn, G.P. Korchemsky and E. Sokatchev, Hexagon Wilson loop = six-gluon MHV amplitude, Nucl. Phys. B 815 (2009) 142 [ar**v:0803.1466] [INSPIRE].
N. Berkovits and J. Maldacena, Fermionic T-duality, Dual Superconformal Symmetry and the Amplitude/Wilson Loop Connection, JHEP 09 (2008) 062 [ar**v:0807.3196] [INSPIRE].
L.J. Mason and D. Skinner, The Complete Planar S-matrix of N = 4 SYM as a Wilson Loop in Twistor Space, JHEP 12 (2010) 018 [ar**v:1009.2225] [INSPIRE].
S. Caron-Huot, Notes on the scattering amplitude/Wilson loop duality, JHEP 07 (2011) 058 [ar**v:1010.1167] [INSPIRE].
A.V. Belitsky, A note on two-loop superloop, Phys. Lett. B 718 (2012) 205 [ar**v:1207.1924] [INSPIRE].
A.V. Belitsky, Nonsinglet pentagons and NMHV amplitudes, Nucl. Phys. B 896 (2015) 493 [ar**v:1407.2853] [INSPIRE].
H. Elvang, D.Z. Freedman and M. Kiermaier, Solution to the Ward Identities for Superamplitudes, JHEP 10 (2010) 103 [ar**v:0911.3169] [INSPIRE].
V.P. Nair, A Current Algebra for Some Gauge Theory Amplitudes, Phys. Lett. B 214 (1988) 215 [INSPIRE].
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. B 828 (2010) 317 [ar**v:0807.1095] [INSPIRE].
S. Caron-Huot, Superconformal symmetry and two-loop amplitudes in planar N = 4 super Yang-Mills, JHEP 12 (2011) 066 [ar**v:1105.5606] [INSPIRE].
G.P. Korchemsky and E. Sokatchev, Superconformal invariants for scattering amplitudes in N = 4 SYM theory, Nucl. Phys. B 839 (2010) 377 [ar**v:1002.4625] [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, JHEP 01 (2011) 041 [ar**v:1008.2958] [INSPIRE].
N. Arkani-Hamed et al., Scattering Amplitudes and the Positive Grassmannian, ar**v:1212.5605 [INSPIRE].
N. Arkani-Hamed and J. Trnka, The Amplituhedron, JHEP 10 (2014) 30 [ar**v:1312.2007] [INSPIRE].
A.V. Belitsky, Fermionic pentagons and NMHV hexagon, Nucl. Phys. B 894 (2015) 108 [ar**v:1410.2534] [INSPIRE].
A. Sever, P. Vieira and T. Wang, OPE for Super Loops, JHEP 11 (2011) 051 [ar**v:1108.1575] [INSPIRE].
A. Sever, P. Vieira and T. Wang, From Polygon Wilson Loops to Spin Chains and Back, JHEP 12 (2012) 065 [ar**v:1208.0841] [INSPIRE].
Tree Heptagon exercise on the first day of the Mathematica Summer School on Theoretical Physics, 6th edition, Porto Portugual (2014), http://msstp.org/?q=node/289.
L.J. Dixon, J.M. Drummond and J.M. Henn, Bootstrap** the three-loop hexagon, JHEP 11 (2011) 023 [ar**v:1108.4461] [INSPIRE].
L.J. Dixon, J.M. Drummond, C. Duhr and J. Pennington, The four-loop remainder function and multi-Regge behavior at NNLLA in planar N = 4 super-Yang-Mills theory, JHEP 06 (2014) 116 [ar**v:1402.3300] [INSPIRE].
L.J. Dixon, J.M. Drummond, C. Duhr, M. von Hippel and J. Pennington, Bootstrap** six-gluon scattering in planar N = 4 super-Yang-Mills theory, PoS(LL2014)077 [ar** an NMHV amplitude through three loops, JHEP 10 (2014) 65 [ar**v:1408.1505] [INSPIRE].
N. Arkani-Hamed, F. Cachazo and J. Kaplan, What is the Simplest Quantum Field Theory?, JHEP 09 (2010) 016 [ar**v:0808.1446] [INSPIRE].
L.J. Mason and D. Skinner, Dual Superconformal Invariance, Momentum Twistors and Grassmannians, JHEP 11 (2009) 045 [ar**v:0909.0250] [INSPIRE].
A. Hodges, Eliminating spurious poles from gauge-theoretic amplitudes, JHEP 05 (2013) 135 [ar**v:0905.1473] [INSPIRE].
J.L. Bourjaily, Efficient Tree-Amplitudes in N = 4: Automatic BCFW Recursion in Mathematica, ar**v:1011.2447 [INSPIRE].
G.P. Korchemsky and E. Sokatchev, Symmetries and analytic properties of scattering amplitudes in N = 4 SYM theory, Nucl. Phys. B 832 (2010) 1 [ar**v:0906.1737] [INSPIRE].
J.L. Bourjaily, S. Caron-Huot and J. Trnka, Dual-Conformal Regularization of Infrared Loop Divergences and the Chiral Box Expansion, JHEP 01 (2015) 001 [ar**v:1303.4734] [INSPIRE].
L.F. Alday and J.M. Maldacena, Comments on operators with large spin, JHEP 11 (2007) 019 [ar**v:0708.0672] [INSPIRE].
N. Beisert, S. He, B.U.W. Schwab and C. Vergu, Null Polygonal Wilson Loops in Full N = 4 Superspace, J. Phys. A 45 (2012) 265402 [ar**v:1203.1443] [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: 1412.1132
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
Basso, B., Caetano, J., Córdova, L. et al. OPE for all helicity amplitudes. J. High Energ. Phys. 2015, 18 (2015). https://doi.org/10.1007/JHEP08(2015)018
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2015)018