Fermionic and parafermionic CFTs with $\widehat{su}(2)$ and $\widehat{su}(3)$ symmetry

Kohki Kawabata

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arXiv · 2411.01926

Fermionic and parafermionic CFTs with $\widehat{su}(2)$ and $\widehat{su}(3)$ symmetry

Kohki Kawabata

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Abstract

We investigate two-dimensional conformal field theories (CFTs) with affine $\widehat{su}(2)$ and $\widehat{su}(3)$ algebra symmetry. Their bosonic modular-invariant partition functions have been fully classified based on the ADE classification. In this work, we extend the classification to include fermionic and parafermionic CFTs with the same affine symmetries, utilizing techniques of fermionization and parafermionization. We find that the fermionic and parafermionic $\widehat{su}(2)$ models are related to non-simply laced Dynkin diagrams.

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hep-th cond-mat.stat-mech cond-mat.str-el

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Kohki Kawabata. 2024-11-04. Fermionic and parafermionic CFTs with $\widehat{su}(2)$ and $\widehat{su}(3)$ symmetry. https://arxiv.org/abs/2411.01926

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