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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMay 30th 2022

    starting something – not ready yet for public consumption, but I need to save

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMay 30th 2022
    • (edited May 30th 2022)

    I am after the relation between Z kZ_k parafermions and SU(2)SU(2)-Chern-Simons/WZW theory.

    The article

    gives the identification

    Z kSU(2) k, Z_k \leftrightarrow SU(2)_k \,,

    i.e. that Z kZ_k parafermions are essentially described by SU(2)SU(2) conformal blocks at level kk.

    But it seems to me that (in their section 2) the authors are neglecting the Chern-Simons level renormalization. Including this would instead seem to give

    Z k+2SU(2) k. Z_{k\color{blue}+2} \leftrightarrow SU(2)_k \,.

    Is this discussed anywhere?

    diff, v2, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJun 14th 2022

    have added these tow references, provividing an integrable model for N\mathbb{Z}_N parafermion anyons:

    the second of these refers to topologically ordered ground states as the “modern day philosopher’s stone”.

    This strikes me as an interesting association, so I have added mentioning of this phrase at topological order (here)

    diff, v4, current

    • CommentRowNumber4.
    • CommentAuthorperezl.alonso
    • CommentTimeAug 6th 2023

    added reference on twisted parafermions

    diff, v6, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeMay 29th 2024

    added these pointers:

    diff, v7, current