Ising-like and Fibonacci-Anyons from KZ-equations
arXiv:2112.07195 · doi:10.1007/JHEP09(2022)015
Abstract
In this work we present solutions to Knizhnik-Zamolodchikov (KZ) equations corresponding to conformal block wavefunctions of non-Abelian Ising- and Fibonacci-Anyons. We solve these equations around regular singular points in configuration space in terms of hypergeometric functions and derive explicit monodromy representations of the braid group action. This confirms the correct non-Abelian statistics of the solutions. One novelty of our approach is that we explicitly keep track of spin basis states and identify conformal blocks uniquely with such states at relevant points in moduli space.
39 pages, 3 figures
References in corpus (10)
- Non-Abelian Anyons and Topological Quantum Computation
- Kramers-Wannier-like duality defects in (3+1)d gauge theories
- Non-Invertible Duality Defects in 3+1 Dimensions
- Symmetries and Strings of Adjoint QCD
- A short introduction to Fibonacci anyon models
- Topological Defects on the Lattice: Dualities and Degeneracies
- Higher central charges and topological boundaries in 2+1-dimensional TQFTs
- Wavefunctions for topological quantum registers
- Chiral correlators of the Ising conformal field theory
- Resonating valence bond realization of spin-1 non-Abelian chiral spin liquid on the torus