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Fibonacci-type orbifold data in Ising modular categories | | Vincentas Mulevicius
; Ingo Runkel
; | | Date: |
2 Oct 2020 | | 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. | | Source: | arXiv, 2010.00932 | | Services: | Forum | Review | PDF | Favorites | |
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