General continuum clockwork

Abstract

Abstract:The continuum clockwork is an extra-dimensional set-up to realize certain features of the clockwork mechanism generating exponentially suppressed or hierarchical couplings of light particles. We study the continuum clockwork in a general scheme in which large volume, warped geometry, and localization of zero modes in extra dimension are described by independent parameters. For this, we propose a generalized 5-dimensional linear dilaton model which can realize such set-up as a solution of the model, and examine the KK spectrum and the couplings of zero modes and massive KK modes to boundarylocalized operators for the bulk graviton, Abelian gauge bosons and periodic scalar fields. We discuss how those KK spectra and couplings vary as a function of the volume, warping and localization parameters, and highlight the behavior in the parameter region corresponding to the clockwork limit. We discuss also the field range of 4-dimensional axions originating from either 5-dimensional periodic scalar field or the 5-th component of an Abelian gauge field, and comment on the limitations of continuum clockwork compared to the discrete clockwork.

Axion clockworks from heterotic M-theory: the QCD-axion and its ultra-light companion

“…This will be explicitely discussed in the next section. From (3.12), we see that the axions from heterotic M-theory are identified as "continuous clockwork axions" as explicitly discussed in [15,17]. The bulk gauge boson mass m A serves as the clockwork parameter for the zero mode coupling hierarchy, while k 1 − k 2 ≡ p controls the clockwork gear (KK mode) masses [17,18].…”

“…Their spectrum and couplings can be obtained from the continuum clockwork lagrangian (3.12). Detailed calculations were carried out in [17]. The analysis indicates that both n-th This is still around 1/M P or quite smaller than 1/M 11 for the known examplesĉ 2 = 6, 7, 10 in [18].…”

Heterotic M-theory from the clockwork perspective

“…A comprehensive discussion can be formulated in the formalism of the general continuum clockwork mechanism (GCCW) as described in Ref. [4].…”

A warped relaxion

“…Further developments regarding the 5D JHEP07(2018)033 continuum limit of the clockwork can be found in refs. [27][28][29][30]. Besides the clockwork, one can also generate a potential of the form in eq.…”

“…Demanding that the right electroweak scale is obtained, we then see from eq. (4.3) that 30) where y andỹ need to be chosen such that eqs. (4.21) and (4.22) for Λ G f as well as the limits discussed below eq.…”