title: Geometrically induced magnetic catalysis and critical dimensions.
abstract: 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 ∝(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.
authors.affiliation: Multidisciplinary Center for Astrophysics and Department of Physics, Instituto Superior Técnico, University of Lisbon, Avenida Rovisco Pais 1, 1049-001 Lisboa, Portugal.
authors.forename: Antonino
authors.initials: A
authors.lastname: Flachi
authors.affiliation: Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan.
authors.forename: Kenji
authors.initials: K
authors.lastname: Fukushima
authors.affiliation: Multidisciplinary Center for Astrophysics and Department of Physics, Instituto Superior Técnico, University of Lisbon, Avenida Rovisco Pais 1, 1049-001 Lisboa, Portugal.
authors.forename: Vincenzo
authors.initials: V
authors.lastname: Vitagliano