On Classification of Modular Tensor Categories Academic Article uri icon

abstract

  • 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 data of the 10 non-trivial prime UMTCs are given in Sect. 5. Relevance of UMTCs to topological quantum computation and various conjectures are given in Sect. 6. The Author(s) 2009.

published proceedings

  • COMMUNICATIONS IN MATHEMATICAL PHYSICS

author list (cited authors)

  • Rowell, E., Stong, R., & Wang, Z.

citation count

  • 161

complete list of authors

  • Rowell, Eric||Stong, Richard||Wang, Zhenghan

publication date

  • December 2009