# Holographic CFT A holographic CFT is one that has a local gravity dual. Such CFTs are expected to have a large central charge and a sparse spectrum of single-trace primary operators (which correspond to matter fields in the bulk dual). In the bulk, it is then expected that, if the bulk EFT has a reasonably small number of particle species, then there is perturbative control. For $\mathcal{N}=4$ SYM at weak coupling, the spectrum is *not* sparse. Then the bulk gravity theory is very stringy and non-local. ## Refs - [[2009#Heemskerk, Penedones, Polchinski, Sully]] - [[2017#Mefford, Shaghoulian, Shyani]] - [[2024#Apolo, Belin, Bintanja]]: strongly coupled AdS matter ## CFT conditions ### Mass gap - large-$N$ + large gap to higher-spin single-trace operators = weakly coupled, local gravity dual - [[2009#Heemskerk, Penedones, Polchinski, Sully]] ### Using chaos - speculation that saturation of chaos bound might be a sufficient condition for a system to have Einstein gravity dual ([[2015#Maldacena, Shenker, Stanford]] and [[Kitaev2014Talk]]) - there are attempts to show this but it turns out not sufficient (only necessary) (see [[2018#Jahnke (Review)]] sec 4.2.2 for refs) ## Spectrum - using radial quantization you can think of the spectrum as either the spectrum of conformal dimensions of primary operators or the energy spectrum of primary states when the theory is quantised on a sphere. - supergravity spectrum ![[Talk201807030001_spectrum.png|500]] - large higher-spin gap = "strong coupling" $\Delta_{\mathrm{gap}} \sim M_\text{HS}$ ## Other related issues - time periodicity: [[CrapsDeClerckEvnin2021]] - extracting excited states?: [[MartinezSilva2021]][](https://arxiv.org/abs/2110.07555) - bulk locality: [[2023#Bahiru, Belin, Papadodimas, Sarosi, Vardian]]