Geometrically induced magnetic catalysis and critical dimensions

TL;DR

This paper explores how magnetic fields and geometry interact in fermionic systems, revealing a new form of magnetic catalysis influenced by curvature and dimensionality, especially around the critical dimension D=4.

Contribution

It introduces the concept of geometrically induced magnetic catalysis arising from higher-order effects mixing magnetic fields and curvature, and identifies D=4 as a critical dimension affecting magnetic shifts.

Findings

Infrared singularity in higher-order terms leads to geometrically induced magnetic catalysis.

Magnetic shift in dynamical mass depends on space-time dimension, changing at D=4.

Curvature regulates the magnetic catalysis effect in interacting fermionic systems.

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 $\propto (4-D)eB$, 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.