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arXiv · 1711.03122

Sparseness bounds on local operators in holographic $CFT_d$

Eric Mefford·Edgar Shaghoulian·Milind Shyani
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Abstract

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 $\rho(\Delta) \lesssim \exp\left(\frac{2\pi\Delta}{d-1}\right)$ for CFT$_d$. 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 $J_i$ and $U(1)$ charge $Q$, obtaining bounds on $\rho(\Delta, J_i, Q)$ in $d=3$ through $6$. All bounds are saturated by black holes at the Hawking-Page transition and vanish beyond the corresponding BPS bound.

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Eric Mefford, Edgar Shaghoulian, Milind Shyani. 2017-11-08. Sparseness bounds on local operators in holographic $CFT_d$. https://doi.org/10.1007/jhep07(2018)051

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