The Gross-Neveu model on a sphere with a magnetic monopole

Details The Gross-Neveu model on a sphere with a magnetic monopole The Gross-Neveu model on a sphere with a magnetic monopole

1996-06-10

arxiv.org/abs/hep-th/9606051v1

Phys.Rev.D54:5010-5013,1996

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX, 9 pages, 3 figures

Scientific paper

10.1103/PhysRevD.54.5010

We study, for the first time, the phase structure of the Gross--Neveu model with a combination of a (constant) gravitational and a magnetic field. This has been made possible by our finding of an exact solution to the problem, namely the effective potential for the composite fermions. Then, from the corresponding implicit equation the phase diagram for the dynamical fermion mass is calculated numerically for some values of the magnetic field. %(what can be done with arbitrary precision). For a small magnetic field the phase diagram hints to the possibility of a second order phase transition at some critical curvature. With growing magnetic field only the phase with broken chiral symmetry survives, because the magnetic field prevents the decay of the chiral condensate. This result is bound to have important consequences in early universe cosmology.

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