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Is the rigid structure needed for describing anyons?

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To describe anyons, it is said that category theory is useful. In my understanding, a category suitable for describing anyons is a modular tensor category, which has a rigid structure. Physically, the rigid structure means that there exists a conjugate type of anyons a* for each type a, which yields a trivial charge when a and a* are fused.

However, I wonder why there should be a conjugate type for each type. What is the physical reasoning or observation for this requirement?

asked Jul 21, 2020 in Theoretical Physics by K_Phys (30 points) [ revision history ]

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