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However, a related theory, where one reverses the direction of the Majorana mode, can be made T invariant. Since this may have an application to 3D topological insulators, it will be discussed in a separate publication
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Sometimes, only theories with k = 0 mod 4 are labeled SO(3)k, since otherwise they are nonmodular. Since we are specifically interested in theories that contain the electron, which are necessarily nonmodular, we will not make this distinction
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This structure is reminiscent of the notion of G action in a braided G-crossed category [37,38]
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It is actually known that the symmetric center Z(C) of any braided fusion category C comes in two types [41]: Either it consists entirely of bosons and is isomorphic to the set of representations of some finite group G, in which case the bulk forms a (possibly twisted) G-gauge theory, or it is a supersymmetric version of this, where G contains some odd elements and the corresponding representations have even and odd sectors, corresponding to bosons and fermions, respectively
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It is actually known that the symmetric center Z(C) of any braided fusion category C comes in two types [41]: Either it consists entirely of bosons and is isomorphic to the set of representations of some finite group G, in which case the bulk forms a (possibly twisted) G-gauge theory, or it is a supersymmetric version of this, where G contains some odd elements and the corresponding representations have even and odd sectors, corresponding to bosons and fermions, respectively
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42
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84893711764
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Indeed, if we take a gauge transformation to act by phase factor βca,b on the fusion space vca,b, then any choice that satisfies βss,s βss,s = i, βss,s βss,s =-i, βss,s βss,s = -i, βss,s βss,s =-i and sets the other βabc to be trivial does the trick. The action of T is then truly onsite
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c to be trivial does the trick. The action of T is then truly onsite.
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44
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A pair of particles that are interchanged by T and have mutual statistics η=±1 will, when fused together, carry T2 =η This may be understood by regarding the action of T2 as taking one particle around the other
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2 as taking one particle around the other
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Related results have been obtained by C. Wang, A. Potter, and T. Senthil (unpublished) in the context of topological insulators
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Related results have been obtained by C. Wang, A. Potter, and T. Senthil (unpublished) in the context of topological insulators.
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