# On Classification of Modular Tensor Categories

@article{Rowell2007OnCO, title={On Classification of Modular Tensor Categories}, author={Eric C. Rowell and R. Stong and Z. Wang}, journal={Communications in Mathematical Physics}, year={2007}, volume={292}, pages={343-389} }

We classify all unitary modular tensor categories (UMTCs) of rank ≤ 4. There are a total of 35 UMTCs of rank ≤ 4 up to ribbon tensor equivalence. Since the distinction between the modular S-matrix S and −S has both topological and physical significance, so in our convention there are a total of 70 UMTCs of rank ≤ 4. In particular, there are two trivial UMTCs with S = (±1). Each such UMTC can be obtained from 10 non-trivial prime UMTCs by direct product, and some symmetry operations. Explicit… Expand

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