Abstract
We consider the higher order clockwork theory of gravitational interactions, whereby a number of gravitons are coupled together with TeV strength, but nevertheless generate a Planck scale coupling to matter without the need for a dilaton. It is shown that the framework naturally lends itself to a five-dimensional geometry, and we find the 5D continuum version of such deconstructed 4D gravitational clockwork models. Moreover, the clockwork picture has matter coupled to particular gravitons, which in the 5D framework looks like a braneworld model, with the Randall-Sundrum model being a special case. More generally, the gravitational clockwork leads to a family of scalar-tensor braneworld models, where the scalar is not a dilaton.
Highlights
The large hierarchy of scales between electroweak physics and gravitational physics remains somewhat of a mystery
It is shown that the framework naturally lends itself to a fivedimensional geometry, and we find the 5D continuum version of such deconstructed 4D gravitational clockwork models
A well-known continuum model was developed by Randall and Sundrum [1], whereby codimension one branes were embedded in an anti–de Sitter (AdS) spacetime, with the result that the effective four-dimensional scale of gravity is a combination of the AdS scale and the five-dimensional scale of gravity
Summary
The large hierarchy of scales between electroweak physics and gravitational physics remains somewhat of a mystery. Clockwork mechanisms were shown to be able to generate exponential hierarchies between the fundamental energy scale and the effective energy scale of the low energy degrees of freedom [2,3] This is achieved by having a number of fields coupled together sequentially, where the coupling between each pair of fields in the sequence is Oð1Þ. The framework of [5], which describes how multiple gravity sectors may be coupled together consistently, was used in [6] to create a model with a discrete number of gravitons, coupled in a clockwork sense This fully nonlinear theory of gravity was able to generate a hierarchy of scales, this time between the single scale appearing in the clockwork action and the Planck scale associated with the massless graviton mode. Having done that we shall see how this naturally leads, in the first instance, to the Randall-Sundrum model and, in more generality, to scalar-tensor braneworld models
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