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arXiv · 2010.00932

Fibonacci-type orbifold data in Ising modular categories

Vincentas Mulevicius·Ingo Runkel
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Abstract

An orbifold datum is a collection $\mathbb{A}$ of algebraic data in a modular fusion category $\mathcal{C}$. It allows one to define a new modular fusion category $\mathcal{C}_{\mathbb{A}}$ in a construction that is a generalisation of taking the Drinfeld centre of a fusion category. Under certain simplifying assumptions we characterise orbifold data $\mathbb{A}$ in terms of scalars satisfying polynomial equations and give an explicit expression which computes the number of isomorphism classes of simple objects in $\mathcal{C}_{\mathbb{A}}$. 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 $E_6$ commutative algebra.

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Vincentas Mulevicius, Ingo Runkel. 2020-10-02. Fibonacci-type orbifold data in Ising modular categories. https://arxiv.org/abs/2010.00932

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