On chiral symmetry breaking in a constant magnetic field in higher dimension

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 → 1 + 1 for even-dimensional spacetimes and D → 0 + 1 for odd-dimensional spacetimes. Explicit solutions of the gap equation confirm our conclusions. (C) 2000 Published by Elsevier Science B.V.