On Classification of Modular Tensor Categories

@inproceedings{Stong2009OnCO,
  title={On Classification of Modular Tensor Categories},
  author={R. Stong and Zhenghan Wang},
  year={2009}
}
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… CONTINUE READING
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