Fibonacci-type orbifold data in Ising modular categories

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.(c) 2022 Elsevier B.V. All rights reserved.