Journal of High Energy Physics

, 2018:177 | Cite as

Hexagonalization of correlation functions II: two-particle contributions

  • Thiago Fleury
  • Shota Komatsu
Open Access
Regular Article - Theoretical Physics


In this work, we compute one-loop planar five-point functions in \( \mathcal{N}=4 \) super-Yang-Mills using integrability. As in the previous work, we decompose the correlation functions into hexagon form factors and glue them using the weight factors which depend on the cross-ratios. The main new ingredient in the computation, as compared to the four-point functions studied in the previous paper, is the two-particle mirror contribution. We develop techniques to evaluate it and find agreement with the perturbative results in all the cases we analyzed. In addition, we consider next-to-extremal four-point functions, which are known to be protected, and show that the sum of one-particle and two-particle contributions at one loop adds up to zero as expected. The tools developed in this work would be useful for computing higher-particle contributions which would be relevant for more complicated quantities such as higher-loop corrections and non-planar correlators.


1/N Expansion Integrable Field Theories Supersymmetric Gauge Theory 


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.


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Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Instituto de Física Teórica, UNESP — Univ. Estadual Paulista, ICTP South American Institute for Fundamental ResearchSão PauloBrasil
  2. 2.Laboratoire de Physique Théorique de l’Ecole Normale Supérieure et l’Université Paris-VIParis CEDEXFrance
  3. 3.International Institute of Physics, Federal University of Rio Grande do NorteNatalBrazil
  4. 4.School of Natural SciencesInstitute for Advanced StudyPrincetonU.S.A.

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