We discuss the effect of baryonic matter on the zero-temperature chiral phase transition at finite chemical potential in the presence of a background magnetic field. The main part of our study is done in the deconfined geometry of the SakaiSugimoto model, i.e. at large N _c and strong coupling, with non-antipodal separation of the flavor branes. We find that for not too large magnetic fields baryonic matter completely removes the chiral phase transition: chirally broken matter persists up to arbitrarily large chemical potential. At sufficiently large magnetic fields, baryonic matter becomes disfavored and mesonic matter is directly superseded by quark matter. In order to discuss the possible relevance of our results to quantum chromodynamics, we compute the baryon onset in a relativistic mean-field model including the anomalous magnetic moment and point out the differences to our holographic calculation.
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