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Local Integrand Representations of All Two-Loop Amplitudes in Planar SYM

Bourjaily, Jacob L. and Trnka, Jaroslav (2015) Local Integrand Representations of All Two-Loop Amplitudes in Planar SYM. Journal of High Energy Physics, 2015 (8). Art. No. 119. ISSN 1126-6708. doi:10.1007/JHEP08(2015)119.

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We use generalized unitarity at the integrand-level to directly construct local, manifestly dual-conformally invariant formulae for all two-loop scattering amplitudes in planar, maximally supersymmetric Yang-Mills theory (SYM). This representation separates contributions into manifestly finite and manifestly divergent terms---in a way that renders all infrared-safe observables (including ratio functions) calculable without any need for regulation. These results perfectly match the all-loop BCFW recursion relations, to which we provide a closed-form solution valid through two-loop-order. Finally, we describe and document a Mathematica package which implements these results, available as part of this work's source files on the arXiv.

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Additional Information:© 2015 The Authors. 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. Article funded by SCOAP3. Received: June 13, 2015; Accepted: July 20, 2015; Published: August 25, 2015. We are very grateful to Simon Caron-Huot for important insights, discussions, and contributions, and to Nima Arkani-Hamed, Zvi Bern, Freddy Cachazo, and Marcus Spradlin for especially fruitful conversations. This work was supported through the hospitality of the Aspen Center for Physics (supported by NSF grant #1066293), the Hong Kong University of Science and Technology’s Institute for Advanced Study, and the California Institute of Technology. This work has been supported in part by the Harvard Society of Fellows, a grant from the Harvard Milton Fund, and a MOBILEX research grant from the Danish Council for Independent Research (JLB); and also by the David and Ellen Lee Postdoctoral Scholarship and by the Department of Energy under grant DE-SC0011632 (JT).
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Hong Kong University of Science and TechnologyUNSPECIFIED
Harvard Society of FellowsUNSPECIFIED
Harvard Milton FundUNSPECIFIED
Danish Council for Independent ResearchMOBILEX
David and Ellen Lee Postdoctoral ScholarshipUNSPECIFIED
Department of Energy (DOE)DE-SC0011632
Subject Keywords:Supersymmetric gauge theory Scattering Amplitudes, 1/N Expansion
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Issue or Number:8
Record Number:CaltechAUTHORS:20150814-090422946
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Official Citation:Journal of High Energy Physics v.2015, no.8; 2015 DOI:10.1007/JHEP08(2015)119 Local integrand representations of all two-loop amplitudes in planar SYM Springer Berlin Heidelberg 2015-08-25
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:59527
Deposited By: Joy Painter
Deposited On:14 Aug 2015 16:20
Last Modified:10 Nov 2021 22:22

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