Abstract
An orbifold datum is a collection A of algebraic data in a modular fusion category C. It allows one to define a new modular fusion category CA in a construction that is a generalisation of taking the Drinfeld centre of a fusion category. Under certain simplifying assumptions we characterise orbifold data A in terms of scalars satisfying polynomial equations and give an explicit expression which computes the number of isomorphism classes of simple objects in CA.In Ising-type modular categories we find new examples of orbifold data which – in an appropriate sense – exhibit Fibonacci fusion rules. The corresponding orbifold modular categories have 11 simple objects, and for a certain choice of parameters one obtains the modular category for sl(2) at level 10. This construction inverts the extension of the latter category by the E6 commutative algebra.
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