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

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.

13 pages, 1 figure; v2: references added, minor corrections made

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Cited by in corpus (7)

• Toric Calabi-Yau threefolds as quantum integrable systems. R-matrix and RTT relations
• Twisted reduction of quiver W-algebras
• Virasoro Constraint for Uglov Matrix Model
• Elliptic algebra, Frenkel-Kac construction and root of unity limit
• NSR singular vectors from Uglov polynomials
• On refined Chern-Simons and refined ABJ matrix models
• Direct Sum Structure of the Super Virasoro Algebra and a Fermion Algebra Arising from the Quantum Toroidal ${\mathfrak{gl}}_2$