Sparseness bounds on local operators in holographic CFTd

  • Eric Mefford
  • Edgar Shaghoulian
  • Milind ShyaniEmail author
Open Access
Regular Article - Theoretical Physics


We use the thermodynamics of anti-de Sitter gravity to derive sparseness bounds on the spectrum of local operators in holographic conformal field theories. The simplest such bound is \( \rho \left(\varDelta \right)\lesssim \exp \left(\frac{2\pi \Delta}{d-1}\right) \) for CFTd. Unlike the case of d = 2, this bound is strong enough to rule out weakly coupled holographic theories. We generalize the bound to include spins Ji and U(1) charge Q, obtaining bounds on ρ, Ji, Q) in d = 3 through 6. All bounds are saturated by black holes at the Hawking-Page transition and vanish beyond the corresponding BPS bound.


AdS-CFT Correspondence Black Holes Conformal Field Theory Gaugegravity correspondence 


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.Department of PhysicsUniversity of CaliforniaSanta BarbaraU.S.A.
  2. 2.Department of PhysicsCornell UniversityIthacaU.S.A.
  3. 3.Stanford Institute for Theoretical PhysicsStanfordU.S.A.

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