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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 Zk parafermions and SU(2)-Chern-Simons/WZW theory.

    The article

    • Daniel C. Cabra, Eduardo Fradkin, G. L. Rossini, F. A. Schaposnik, Section 4 of: Non-Abelian fractional quantum Hall states and chiral coset conformal field theories, International Journal of Modern Physics A 15 30 (2000) 4857-4870 [doi:10.1142/S0217751X00002354, arXiv:cond-mat/9905192]

    gives the identification

    ZkSU(2)k,

    i.e. that Zk parafermions are essentially described by SU(2) conformal blocks at level k.

    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

    Zk+2SU(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 parafermion anyons:

    • A. M. Tsvelik, An integrable model with parafermion zero energy modes, Phys Rev. Lett. 113 066401 (2014) [arXiv:1404.2840, doi:10.1103/PhysRevLett.113.066401]

    • A. M. Tsvelik, ZN parafermion zero modes without Fractional Quantum Hall effect [arXiv:1407.4002]

    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