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In the Hall effect, the edge modes that possess an anomaly are connected to the bulk in such a way that the total system is gauge invariant and and has a conserved current. The Bardeen Zumino consistancy conditions arise from considering the current $J_{\mu {\rm consistent}}$ as the functional derivative with respect to $A_\mu$ of the edge effective action ...


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There is an important distinction here which I feel the other answers have not addressed. One can check that the unitary $U$ as given in the question is indeed symmetric in the sense that $[U,W(g)] = 0$, where $W(g)$ is the representation of the symmetry. It is also a local unitary, in the sense that one can find a local (possibly time-dependent) Hamiltonian ...


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The definition in terms of LU transformations is more fundamental. In the general case, we believe that topological orders are described by modular tensor categories (MTC), and the equivalence of topological orders translates into the equivalence of MTCs. In the special case of boundary-gapped topological orders, they are all realized by quantum double (also ...



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