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We study various aspects of fermions and their chiral condensates, both inthe bulk of AdS4 spacetime and in the dual boundary theory. For the most part,we focus on a geometry with an infra-red hard wall. We show that, contrary tocommon lore, there exist boundary conditions in which the hard wall gives riseto a discrete, but gapless, fermionic spectrum. In such a setting, the presenceof a magnetic field induces a bulk fermion condensate which spontaneouslybreaks CP invariance. We develop the holographic dictionary between compositeoperators and show that this bulk condensate has the interpretation of boundarymagnetic catalysis involving a double-trace operator. Finally, we explain howone can replace the hard wall with bulk magnetic monopoles. In such aframework, magnetic catalysis can be viewed as a consequence of theCallan-Rubakov effect.

A Gapless Hard Wall: Magnetic Catalysis in Bulk and Boundary