Clockwork Goldstone bosons

The clockwork mechanism has recently been proposed as a natural way to generate hierarchies among parameters in quantum field theories. The mechanism is characterized by a very specific pattern of spontaneous and explicit symmetry breaking, and the presence of new light states referred to as "gears." In this paper we begin by investigating the self-interactions of these gears in a scalar clockwork model and find a paritylike selection rule at all orders in the fields. We then proceed to investigate how the clockwork mechanism can be realized in five-dimensional linear dilaton models from the spontaneous symmetry breaking of a complex bulk scalar field. We also discuss how the clockwork mechanism is manifest in the scalar components of five-dimensional gauge theories in the linear dilaton model, and build their four-dimensional deconstructed analogue. Finally we discuss attempts at building both four-dimensional and five-dimensional realizations of a non-Abelian scalar clockwork mechanism, where in the latter we consider scenarios in which the Goldstone bosons arise from five-dimensional scalar and five-dimensional gauge fields.