  Parity and CP symmetries are broken in the world around us. Nonetheless,
parity (or CP) may be a gauge symmetry which is higgsed in our universe. This
is assumed in many scenarios for physics beyond the Standard Model, including
the classic Nelson--Barr proposal for the Strong CP problem. Gauged parity can
only arise in quantum gravity, where it corresponds to a path integral over
both orientable and non-orientable spacetime manifolds. We show that
spontaneous breaking of gauged parity leads to exactly stable domain walls, and
describe the implications for the cosmology of models with gauged parity. These
domain walls carry an unusual sort of charge, which superficially has features
in common with both gauge charges and global charges. We show that these
unusual charges are consistent with the expected absence of global symmetries
in quantum gravity when there exists a complete spectrum of dynamical objects
required by the Swampland Cobordism Conjecture, including end-of-the-world
branes.
