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Journal of High Energy Physics

, 2017:130 | Cite as

Hexagonalization of correlation functions

  • Thiago FleuryEmail author
  • Shota Komatsu
Open Access
Regular Article - Theoretical Physics

Abstract

We propose a nonperturbative framework to study general correlation functions of single-trace operators in \( \mathcal{N} \) = 4 supersymmetric Yang-Mills theory at large N . The basic strategy is to decompose them into fundamental building blocks called the hexagon form factors, which were introduced earlier to study structure constants using integrability. The decomposition is akin to a triangulation of a Riemann surface, and we thus call it hexagonalization. We propose a set of rules to glue the hexagons together based on symmetry, which naturally incorporate the dependence on the conformal and the R-symmetry cross ratios. Our method is conceptually different from the conventional operator product expansion and automatically takes into account multi-trace operators exchanged in OPE channels. To illustrate the idea in simple set-ups, we compute four-point functions of BPS operators of arbitrary lengths and correlation functions of one Konishi operator and three short BPS operators, all at one loop. In all cases, the results are in perfect agreement with the perturbative data. We also suggest that our method can be a useful tool to study conformal integrals, and show it explicitly for the case of ladder integrals.

Keywords

1/N Expansion AdS-CFT Correspondence Integrable Field Theories Supersymmetric gauge theory 

Notes

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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© The Author(s) 2017

Open AccessThis 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.

Authors and Affiliations

  1. 1.Instituto de Física Teórica, UNESP — Univ. Estadual PaulistaICTP South American Institute for Fundamental ResearchSão PauloBrasil
  2. 2.Perimeter Institute for Theoretical PhysicsOntarioCanada

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