Baryonic matter at strong coupling: confining superfluids and deconfined ferromagnets

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.