  We introduce a model of dark matter (DM) where the DM is a composite of a
spontaneously broken conformal field theory. The DM is a thermal relic with its
abundance determined by the freeze-out of annihilations to dilatons, the
Goldstone boson of broken conformal symmetry. If the dilaton is heavier than
the DM this is an example of forbidden DM. We explore the phenomenology of this
model in its 5D dual description, corresponding to a warped extra dimension
with the Standard Model on the ultraviolet brane and the DM on the infrared
brane. We find the model is compatible with theoretical and experimental
constraints for DM masses in the $0.1$-$10$ GeV range. The conformal phase
transition is supercooled and strongly first-order. It can source large
stochastic gravitational wave signals consistent with those recently observed
at pulsar timing arrays like NANOGrav. The majority of the viable parameter
space will be probed by future detectors designed to search for long-lived
particles, including most of the region favored by the NANOGrav signal. The
rest of the parameter space can be probed at future direct detection
experiments.
