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I was digging into Nielson-Ninomiya Theorem and doubler fermions, as well as solutions to these problems using Domain Wall Fermions and overlap lattice fermions, both of which make effective use of a 5th dimension.

Does this imply that our universe is either a continuous 3+1 dimensional space, or a space that is 4+1 dimensions on a lattice?

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It might actualy be, 5DLQCD or GTFO, but either will do. –  user3955 Jun 10 '11 at 1:22
    
Even most lattice theorists wouldn't say that the real world is 4+1-dimensional and can be defined on a lattice, but that they are working with effective field theories that should be studied in the limit of a large cutoff. –  Gerben Jun 10 '11 at 12:42

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