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}
}
• Published 2007
• Mathematics, Physics
• Communications in Mathematical Physics
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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