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The construction of CP-invariant lattice chiral gauge theories and theconstruction of lattice Majorana fermions with chiral Yukawa couplings issubject to topological obstructions. In the present work we suggest latticeextensions of charge and parity transformation for Weyl fermions. This enablesus to construct lattice chiral gauge theories that are CP invariant. For theconstruction of Majorana-Yukawa couplings, we discuss two models withsymplectic Majorana fermions: a model with two symplectic doublets, and onewith an auxiliary doublet.

CP invariance of chiral gauge theories and Majorana-Yukawa couplings on the lattice