In de Sitter space with a background magnetic field, the field catalyzes chiral symmetry breaking while Hubble curvature restores it, with a second-order phase boundary.
Dimensional Reduction and Dynamical Chiral Symmetry Breaking by a Magnetic Field in $3+1$ Dimensions
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abstract
It is shown that in $3+1$ dimensions, a constant magnetic field is a catalyst of dynamical chiral symmetry breaking, leading to generating a fermion mass even at the weakest attractive interaction between fermions. The essence of this effect is the dimensional reduction $D \rightarrow D-2$ ($3+1 \rightarrow 1+1$) in the dynamics of fermion pairing in a magnetic field. The effect is illustrated in the Nambu-Jona-Lasinio model. Possible applications of this effect are briefly discussed.
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Magnetic Catalysis and Fermion Mass Generation in de Sitter Spacetime
In de Sitter space with a background magnetic field, the field catalyzes chiral symmetry breaking while Hubble curvature restores it, with a second-order phase boundary.