Sparseness bounds on local operators in holographic CFT_{ d }
Abstract
We use the thermodynamics of antide Sitter gravity to derive sparseness bounds on the spectrum of local operators in holographic conformal field theories. The simplest such bound is ρ (Δ)≲ \exp (2π Δ/d1) 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 ρ(Δ , J _{ i } , Q) in d = 3 through 6. All bounds are saturated by black holes at the HawkingPage transition and vanish beyond the corresponding BPS bound.
 Publication:

Journal of High Energy Physics
 Pub Date:
 July 2018
 DOI:
 10.1007/JHEP07(2018)051
 arXiv:
 arXiv:1711.03122
 Bibcode:
 2018JHEP...07..051M
 Keywords:

 AdSCFT Correspondence;
 Black Holes;
 Conformal Field Theory;
 Gaugegravity correspondence;
 High Energy Physics  Theory
 EPrint:
 21 pages, 9 figures, 2 appendices