  We propose a brane-world setup based on gauge/gravity duality that permits
the simultaneous realisation of self-tuning of the cosmological constant and a
stabilisation of the electroweak hierarchy. The Standard Model dynamics
including the Higgs sector is confined to a flat 4-dimensional brane, embedded
in a 5-dimensional bulk whose dynamics is governed by Einstein-dilaton-axion
gravity. The inclusion of a dynamical bulk axion is new compared to previous
implementations of the self-tuning mechanism. Because of the presence of the
axion, the model generically exhibits a multitude of static solutions, with
different values for the equilibrium position for the brane. Under mild
assumptions regarding the dependence of brane parameters on bulk fields, a
number of these solutions exhibit electroweak symmetry breaking with a
hierarchically small Higgs mass as compared to the cutoff-scale of the brane
theory. The realisation of self-tuning of the cosmological constant is generic
and as efficient as in previous constructions without a bulk axion. Vacua with
a hierarchically small Higgs mass can sometimes be found, regardless of whether
the brane theory depends explicitly on the bulk axion. Because it is expected
on general principles that the brane action will depend on the axion, the
generation of solutions with a large hierarchy is a robust feature.
