Four-point conformal blocks with three heavy background operators

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


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.


AdS-CFT Correspondence Conformal Field Theory 


Open Access

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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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