On Chiral Symmetry Breaking in a Constant Magnetic Field in Higher Dimension

TL;DR

This paper investigates how a constant magnetic field influences chiral symmetry breaking in higher-dimensional Nambu-Jona-Lasinio models, revealing effective dimensional reduction in the infrared region for even and odd dimensions.

Contribution

It demonstrates that magnetic fields in higher dimensions can be characterized by multiple parameters and induce effective dimensional reduction, confirmed through explicit gap equation solutions.

Findings

Magnetic field parameters depend on spacetime dimension D

Effective reduction to 1+1 dimensions for even D

Reduction to 0+1 dimensions for odd D

Abstract

Chiral symmetry breaking in the Nambu-Jona-Lasinio model in a constant magnetic field is studied in spacetimes of dimension D > 4. It is shown that a constant magnetic field can be characterized by [(D-1)/2] parameters. For the maximal number of nonzero field parameters, we show that there is an effective reduction of the spacetime dimension for fermions in the infrared region D $\to$ 1 + 1 for even-dimensional spacetimes and D $\to$ 0 + 1 for odd-dimensional spacetimes. Explicit solutions of the gap equation confirm our conclusions.