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arXiv · 1408.4216

$q$-Virasoro/W Algebra at Root of Unity and Parafermions

Hiroshi Itoyama·Takeshi Oota·Reiji Yoshioka
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Abstract

We demonstrate that the parafermions appear in the $r$-th root of unity limit of $q$-Virasoro/$W_n$ algebra. The proper value of the central charge of the coset model $ \frac{\widehat{\mathfrak{sl}}(n)_r \oplus \widehat{\mathfrak{sl}}(n)_{m-n}}{\widehat{\mathfrak{sl}}(n)_{m-n+r}}$ is given from the parafermion construction of the block in the limit.

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Hiroshi Itoyama, Takeshi Oota, Reiji Yoshioka. 2014-08-29. $q$-Virasoro/W Algebra at Root of Unity and Parafermions. https://doi.org/10.1016/j.nuclphysb.2014.10.006

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