# Sparseness bounds on local operators in holographic CFTd

@article{Mefford2018SparsenessBO,
title={Sparseness bounds on local operators in holographic CFTd},
author={Eric Mefford and Edgar Shaghoulian and Milind Shyani},
journal={Journal of High Energy Physics},
year={2018},
volume={2018},
pages={1-28}
}
• Published 8 November 2017
• Physics
• Journal of High Energy Physics
A bstractWe 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 ρΔ≲exp2πΔd−1$$\rho \left(\varDelta \right)\lesssim \exp \left(\frac{2\pi \Delta}{d-1}\right)$$ 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(Δ, Ji, Q) in…
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