A Gapless Hard Wall: Magnetic Catalysis in Bulk and Boundary

TL;DR

This paper explores magnetic catalysis and fermionic spectra in AdS4 with a hard wall, revealing gapless boundary states and spontaneous CP breaking induced by magnetic fields, with implications for holography and monopole physics.

Contribution

It demonstrates the existence of gapless fermionic spectra with specific boundary conditions and connects magnetic catalysis to boundary operators and monopole effects in holography.

Findings

Existence of gapless fermionic spectra with certain boundary conditions.

Magnetic field induces a bulk fermion condensate breaking CP symmetry.

Reformulation of magnetic catalysis via bulk monopoles and the Callan-Rubakov effect.

Abstract

We study various aspects of fermions and their chiral condensates, both in the 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 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.