Two roads to antispacetime in polar distorted B phase: Kibble wall and half-quantum vortex

We consider the emergent tetrad gravity and the analog of antispacetime realized in the recent experiments ( J.T. Makinen, et al., Nat. Comm. 10, 237 (2019)) on the composite defects in superfluid $^3$He: the Kibble walls bounded by strings (the half quantum vortices). The antispacetime can be reached in two different ways: by the "safe" route around the Alice string or by dangerous route across the Kibble wall. This consideration also suggests the scenario of the formation of the discrete symmetry -- the parity $P$ in Dirac equations -- from the continuous symmetry existing on the more fundamental level.

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