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A cardy formula for three-point coefficients or how the black hole got its spots

  • Per Kraus
  • Alexander MaloneyEmail author
Open Access
Regular Article - Theoretical Physics

Abstract

Modular covariance of torus one-point functions constrains the three point function coefficients of a two dimensional CFT. This leads to an asymptotic formula for the average value of light-heavy-heavy three point coefficients, generalizing Cardy’s formula for the high energy density of states. The derivation uses certain asymptotic properties of one-point conformal blocks on the torus. Our asymptotic formula matches a dual AdS3 computation of one point functions in a black hole background. This is evidence that the BTZ black hole geometry emerges upon course-graining over a suitable family of heavy microstates.

Keywords

AdS-CFT Correspondence Conformal Field Theory Black Holes in String Theory Gauge-gravity 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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Copyright information

© The Author(s) 2017

Authors and Affiliations

  1. 1.Department of Physics and AstronomyUniversity of CaliforniaLos AngelesU.S.A.
  2. 2.Physics DepartmentMcGill UniversityMontréalCanada

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