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Classical conformal blocks and accessory parameters from isomonodromic deformations

  • Máté Lencsés
  • Fábio Novaes
Open Access
Regular Article - Theoretical Physics

Abstract

Classical conformal blocks appear in the large central charge limit of 2D Virasoro conformal blocks. In the AdS3/CFT2 correspondence, they are related to classical bulk actions and used to calculate entanglement entropy and geodesic lengths. In this work, we discuss the identification of classical conformal blocks and the Painlevé VI action showing how isomonodromic deformations naturally appear in this context. We recover the accessory parameter expansion of Heun’s equation from the isomonodromic τ -function. We also discuss how the c = 1 expansion of the τ -function leads to a novel approach to calculate the 4-point classical conformal block.

Keywords

Conformal Field Theory Integrable Field Theories AdS-CFT Correspondence 

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) 2018

Authors and Affiliations

  1. 1.International Institute of PhysicsFederal University of Rio Grande do NorteNatal-RNBrazil

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