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Exact correlation functions in conformal fishnet theory

  • Nikolay GromovEmail author
  • Vladimir Kazakov
  • Gregory Korchemsky
Open Access
Regular Article - Theoretical Physics

Abstract

We compute exactly various 4−point correlation functions of shortest scalar operators in bi-scalar planar four-dimensional “fishnet” CFT. We apply the OPE to extract from these functions the exact expressions for the scaling dimensions and the structure constants of all exchanged operators with an arbitrary Lorentz spin. In particular, we determine the conformal data of the simplest unprotected two-magnon operator analogous to the Konishi operator, as well as of the one-magnon operator. We show that at weak coupling 4−point correlation functions can be systematically expanded in terms of harmonic polylogarithm functions and verify our results by explicit calculation of Feynman graphs at a few orders in the coupling. At strong coupling we obtain that the correlation functions exhibit the scaling behaviour typical for semiclassical description hinting at the existence of the holographic dual.

Keywords

AdS-CFT Correspondence Conformal Field Theory Integrable Field Theories 

Notes

Open Access

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© The Author(s) 2019

Authors and Affiliations

  1. 1.Mathematics DepartmentKing’s College LondonLondonU.K.
  2. 2.St.Petersburg INPGatchinaRussia
  3. 3.Laboratoire de Physique Théorique, Département de Physique de l’ENSParisFrance
  4. 4.Université Paris-VI, PSL Research University, Sorbonne UniversitésParisFrance
  5. 5.Institut de Physique Théorique, Unité Mixte de Recherche 3681 du CNRS, Université Paris Saclay, CNRS, CEAGif-sur-YvetteFrance

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