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Topological quasiparticles and the holographic bulk-edge relation in 2+1D string-net models
String-net models allow us to systematically construct and classify 2+1D
topologically ordered states which can have gapped boundaries. We can use a
simple ideal string-net wavefunction, which is described by a set of F-matrices
[or more precisely, a unitary fusion category (UFC)], to study all the
universal properties of such a topological order. In this paper, we describe a
finite computational method -- Q-algebra approach, that allows us to compute
the non-Abelian statistics of the topological excitations [or more precisely,
the unitary modular tensor category (UMTC)], from the string-net wavefunction
(or the UFC). We discuss several examples, including the topological phases
described by twisted gauge theory (i.e., twisted quantum double ).
Our result can also be viewed from an angle of holographic bulk-boundary
relation. The 1+1D anomalous topological orders, that can appear as edges of
2+1D topological states, are classified by UFCs which describe the fusion of
quasiparticles in 1+1D. The 1+1D anomalous edge topological order uniquely
determines the 2+1D bulk topological order (which are classified by UMTC). Our
method allows us to compute this bulk topological order (i.e., the UMTC) from
the anomalous edge topological order (i.e., the UFC).Comment: 32 pages, 8 figures, reference updated, some refinement
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