Geometrically induced magnetic catalysis and critical dimensions

We discuss the combined effect of magnetic fields and geometry in interacting fermionic systems. At leading order in the heat-kernel expansion, the infrared singularity (that in flat space leads to the magnetic catalysis) is regulated by the chiral gap effect, and the catalysis is deactivated by the effect of the scalar curvature. We discover that an infrared singularity is found in higher-order terms that mix the magnetic field with curvature, and these lead to a novel form of geometrically induced magnetic catalysis. The dynamical mass squared is then modified not only due to the chiral gap effect by an amount proportional to the curvature, but also by a magnetic shift $\propto (4-D)eB$, where $D$ represents the number of space-time dimensions. We argue that $D=4$ is a critical dimension across which the behavior of the magnetic shift changes qualitatively.Comment: 5 pages; minor change

Chiral Phase Transitions around Black Holes

In this paper we discuss the possibility that chiral phase transitions, analogous to those of QCD, occur in the vicinity of a black hole. If the black hole is surrounded by a gas of strongly interacting particles, an inhomogeneous condensate will form. We demonstrate this by explicitly constructing self-consistent solutions.Comment: 4 pages; 3 figure

Fermion vacuum energies in brane world models

The fermion representations and boundary conditions in five dimensional anti de Sitter space are described in detail. In each case the one loop effective action is calculated for massless fermions. The possibility of topological or Wilson loop symmetry breaking is discussed.Comment: 6 pages, no figures, one correctio