The dynamics of fermions in curved spacetime is governed by a spin connection, a part of which is contorsion, an auxiliary field independent of the metric, without dynamics but fully expressible in terms of the axial current density of fermions. Its effect is the appearance of a quartic interaction involving all fermions. Contorsion can couple to left and right-handed fermions with different strengths, leading to an effective mass for fermions propagating on a background containing fermionic matter.
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