Building on [1], we examine a holographic model in which a U(1) symmetry and
translational invariance are broken spontaneously at the same time. The
symmetry breaking is realized through the St\"{u}ckelberg mechanism, and leads
to a scalar condensate and a charge density which are spatially modulated and
exhibit unidirectional stripe order. Depending on the choice of parameters, the
oscillations of the scalar condensate can average out to zero, with a frequency
which is half of that of the charge density. In this case the system realizes
some of the key features of pair density wave order. The model also admits a
phase with co-existing superconducting and charge density wave orders, in which
the scalar condensate has a uniform component. In our construction the various
orders are intertwined with each other and have a common origin. The fully
backreacted geometry is computed numerically, including for the case in which
the theory contains axions. The latter can be added to explicitly break
translational symmetry and mimic lattice-type effects.Comment: 37 pages, 17 figure
