Light holographic dilatons near critical points

We investigate the relation between the emergence of a dilaton in gapped (confining) field theories, and the presence of either complex fixed points or instabilities in the strongly coupled dynamics in two classes of bottom-up holographic models. We demonstrate that in one of the two classes there is a critical line of first-order phase transitions (at zero temperature) that terminates at a critical point. We calculate the mass spectrum of fluctuations of the associated regular gravity backgrounds, which we interpret as bound states in the dual field theories. In proximity to the second-order phase transition, we find a parametrically light scalar state, and its composition leads us to identify it as a dilaton.