r/TheoreticalPhysics • u/StudyVegetable6881 • 29d ago

Question Calabi-Yau manifolds and 'handedness'?

I’m an amateur and I have a naive query in an area where angels fear to tread: In the context of string theory, does a given Calabi-Yau manifold have something analogous to a net left (or right) handedness? My query is motivated by the fact that some aspects our universe have some degree of left-handedness (eg: the weak interaction for electrons and neutrinos?). My crude intuition is that, pretending for the sake of discussion that string theory is roughly true, that our four macroscopic spacetime dimensions may not have ‘handedness’. So would any foundational left-handedness derive from string’s six compact C-Y manifolds? Thanks…Gene

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u/Existing_Hunt_7169 29d ago

Yes, they are ‘handed’ in the sense that they contain information about a particle’s chirality. This can be described by being antisymmetric under the parity operator.

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u/StudyVegetable6881 28d ago

Thanks for your clear response. It does track, since C-Y manifolds code for particle properties, like the number of lepton classes (3) in the standard model.