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Four-point conformal blocks with three heavy background operators

  • Konstantin AlkalaevEmail author
  • Mikhail Pavlov
Open Access
Regular Article - Theoretical Physics

Abstract

We study CFT2 Virasoro conformal blocks of the 4-point correlation function \( \left\langle {\mathcal{O}}_L{\mathcal{O}}_H{\mathcal{O}}_H{\mathcal{O}}_H\right\rangle \) with three background operators \( \mathcal{O} \)H and one perturbative operator \( \mathcal{O} \)L of dimensions ΔLH ≪ 1. The conformal block function is calculated in the large central charge limit using the monodromy method. From the holographic perspective, the background operators create AdS3 space with three conical singularities parameterized by dimensions ΔH, while the perturbative operator corresponds to the geodesic line stretched from the boundary to the bulk. The geodesic length calculates the perturbative conformal block. We propose how to address the block/length correspondence problem in the general case of higher-point correlation functions \( \left\langle {\mathcal{O}}_L\cdots {\mathcal{O}}_L{\mathcal{O}}_H\cdots {\mathcal{O}}_H\right\rangle \) with arbitrary numbers of background and perturbative operators.

Keywords

AdS-CFT Correspondence Conformal Field 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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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.I.E. Tamm Department of Theoretical PhysicsP.N. Lebedev Physical InstituteMoscowRussia
  2. 2.Department of General and Applied PhysicsMoscow Institute of Physics and TechnologyDolgoprudnyiRussia

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