Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 342 / 1 / d

Since $\det M=-3$, the condensed top-sector anyons modulo local particles formwhich has order $|\det M|=3$. The same lower bound follows directly from Wilson-operator algebra. TakeBecausetheir crossing operators obeyActing repeatedly with one operator on an eigenstate of the other produces three states with distinct eigenvalues; they are linearly independent and have the same energy. HenceFor these identical maximal boundaries the bound is saturated, although only the lower bound was requested.