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Classical integrability for three-point functions: cognate structure at weak and strong couplings

  • Yoichi Kazama
  • Shota Komatsu
  • Takuya NishimuraEmail author
Regular Article - Theoretical Physics

Abstract

In this paper, we develop a new method of computing three-point functions in the SU(2) sector of the \( \mathcal{N}=4 \) super Yang-Mills theory in the semi-classical regime at weak coupling, which closely parallels the strong coupling analysis. The structure threading two disparate regimes is the so-called monodromy relation, an identity connecting the three-point functions with and without the insertion of the monodromy matrix. We shall show that this relation can be put to use directly for the semi-classical regime, where the dynamics is governed by the classical Landau-Lifshitz sigma model. Specifically, it reduces the problem to a set of functional equations, which can be solved once the analyticity in the spectral parameter space is specified. To determine the analyticity, we develop a new universal logic applicable at both weak and strong couplings. As a result, compact semi-classical formulas are obtained for a general class of three-point functions at weak coupling including the ones whose semi-classical behaviors were not known before. In addition, the new analyticity argument applied to the strong coupling analysis leads to a modification of the integration contour, producing the results consistent with the recent hexagon bootstrap approach. This modification also makes the Frolov-Tseytlin limit perfectly agree with the weak coupling form.

Keywords

AdS-CFT Correspondence Integrable Field Theories 

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) 2016

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

  • Yoichi Kazama
    • 1
    • 2
    • 3
  • Shota Komatsu
    • 4
  • Takuya Nishimura
    • 3
    Email author
  1. 1.Research Center for Mathematical PhysicsRikkyo UniversityTokyoJapan
  2. 2.Quantum Hadron Physics Laboratory, RIKEN Nishina CenterWakoJapan
  3. 3.Institute of PhysicsUniversity of TokyoTokyoJapan
  4. 4.Perimeter Institute for Theoretical PhysicsWaterlooCanada

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