A gapless hard wall: magnetic catalysis in bulk and boundary

We study various aspects of fermions and their chiral condensates, both in the bulk of AdS(4) 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 to common lore, there exist boundary conditions in which the hard wall gives rise to a discrete, but gapless, fermionic spectrum. In such a setting, the presence of a magnetic field induces a bulk fermion condensate which spontaneously breaks CP invariance. We develop the holographic dictionary between composite operators and show that this bulk condensate has the interpretation of boundary magnetic catalysis involving a double-trace operator. Finally, we explain how one can replace the hard wall with bulk magnetic monopoles. In such a framework, magnetic catalysis can be viewed as a consequence of the Callan-Rubakov effect.