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Chiral conformal field theories and gapless edges of 2+1D topological orders

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Chiral conformal field theories and gapless edges of 2+1D topological orders
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16
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In this talk, I will give a positive answer to the following question: given a modular tensor category C, is there a mathematical structure such that its center is C? This question is crucial to the question of how to extend Reshetikhin-Turaev TQFT’s down to points. The idea comes from physics, more precisely, from the boundary-bulk relation of 2d topological orders with a chiral gapless edge. It was long believed that such an edge is described by a chiral conformal field theory. The key is to make this statement mathematically precise.