  We study the phase diagram of a strongly coupled confining theory in $2+1$
dimensions, as a function of temperature and baryon chemical potential. The
theory has a fully fledged supergravity holographic dual, that we use to
predict a line of first order phase transitions separating a confining phase
and a deconfined phase. Both phases exhibit a non-zero baryon density thus
providing a first example of baryonic matter in a confining string dual that
does not require the introduction of flavor branes. We argue that the confining
phase is a baryon superfluid, while the deconfined phase has non-zero baryon
magnetization.
