The holographic entropy zoo

  • Alex MayEmail author
  • Eliot Hijano
Open Access
Regular Article - Theoretical Physics


We study the holographic dual of a two parameter family of quantities known as the α-z divergences. Many familiar information theoretic quantities occur within this family, including the relative entropy, fidelity, and collision relative entropy. We find explicit bulk expressions for the boundary divergences to second order in a state perturbation whenever α is an integer and z ≥ 0, as well as when z ∈ {0, ∞} and α ∈ ℝ. Our results apply for perturbations around an arbitrary background state and in any dimension, under the assumption of the equality of bulk and boundary modular flows.


AdS-CFT Correspondence Classical Theories of Gravity Conformal Field Theory 


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) 2018

Authors and Affiliations

  1. 1.The University of British ColumbiaVancouverCanada

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