Forbidden conformal dark matter at a GeV

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.