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Your statement itself is not quite right. What is not conserved is the chiral current, namely the current of fermions at one of the Weyl nodes. The physics can be understood essentially in one-dimensional version of the Weyl metal: consider a 1D electron gas. There are two Fermi points, and the low-energy theory is given by two "Weyl fermions" in 1D with ...

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To make the math work. Ever since Einstein determined that time is actually another dimension, Physicists have used that notion to expand the conception of the Universe to include added (by not sensible) dimensions to get their math and theories to work. Of particular note is Witten's unification of string theories which "only" required the addition of yet ...

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There seems to be some confusion. In the referenced paper there is no temporal direction, and even though there is curvature there, it has nothing to do with gravity (there is no time). Where as when you compare with $2D$ gauge theory, one of those $2$ dimensions is temporal in deed. So if you wanted to carry the analogy you should consider two dimensions, ...

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There are a few different ways to see that the bosonic string lives in $D=26$. This, by the way, is known as the critical dimension of the theory. I'll give a brief sketch the answer, a more complete one can be found in any textbook, but in particular Polchinski's. Classically, the Polyakov action has 3 main symmetries. These are: 1) Lorentz invariance of ...

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