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I am after the relation between Zk parafermions and SU(2)-Chern-Simons/WZW theory.
The article
gives the identification
Zk↔SU(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+2↔SU(2)k.Is this discussed anywhere?
have added these tow references, provividing an integrable model for ℤN 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)
added these pointers:
Doron Gepner, New conformal field theories associated with Lie algebras and their partition functions, Nuclear Physics B 290 (1987) 10-24 [doi:10.1016/0550-3213(87)90176-3]
Peter Bouwknegt, Bolin Han, Coupled free fermion conformal field theories [arXiv:2403.03471]
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