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String-net models allow us to systematically construct and classify 2+1Dtopologically ordered states which can have gapped boundaries. We can use asimple ideal string-net wavefunction, which is described by a set of F-matrices[or more precisely, a unitary fusion category (UFC)], to study all theuniversal properties of such a topological order. In this paper, we describe afinite computational method -- Q-algebra approach, that allows us to computethe 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 phasesdescribed by twisted gauge theory (i.e., twisted quantum double $D^\alpha(G)$).Our result can also be viewed from an angle of holographic bulk-boundaryrelation. The 1+1D anomalous topological orders, that can appear as edges of2+1D topological states, are classified by UFCs which describe the fusion ofquasiparticles in 1+1D. The 1+1D anomalous edge topological order uniquelydetermines the 2+1D bulk topological order (which are classified by UMTC). Ourmethod allows us to compute this bulk topological order (i.e., the UMTC) fromthe anomalous edge topological order (i.e., the UFC).

Topological quasiparticles and the holographic bulk-edge relation in 2+1D string-net models