  The Sakai-Sugimoto model is the most pre-eminent model of holographic QCD, in
which baryons correspond to topological solitons in a five-dimensional bulk
spacetime. Recently it has been shown that a single soliton in this model can
be well approximated by a flat-space self-dual Yang-Mills instanton with a
small size, although studies of multi-solitons and solitons at finite density
are currently beyond numerical computations. A lower-dimensional analogue of
the model has also been studied in which the Sakai-Sugimoto soliton is replaced
by a baby Skyrmion in three spacetime dimensions with a warped metric. The
lower dimensionality of this model means that full numerical field calculations
are possible, and static multi-solitons and solitons at finite density were
both investigated, in particular the baryonic popcorn phase transitions at high
densities. Here we present and investigate an alternative lower-dimensional
analogue of the Sakai-Sugimoto model in which the Sakai-Sugimoto soliton is
replaced by an $O(3)$-sigma model instanton in a warped three-dimensional
spacetime stabilised by a massive vector meson. A more detailed range of
baryonic popcorn phase transitions are found, and the low-dimensional model is
used as a testing ground to check the validity of common approximations made in
the full five-dimensional model, namely approximating fields using their
flat-space equations of motion, and performing a leading order expansion in the
metric.
