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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | https://arxiv.org/abs/2512.11628 |
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| _version_ | 1866909958606422016 |
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| author | Zang, Yichi |
| author_facet | Zang, Yichi |
| contents | We study irregular representations of Virasoro algebra associated with half-integer order singularities, which arise naturally in the 2d CFT description of Argyres-Douglas theories of type $(A_1, A_{\text{even}})$ and $(A_1, D_{\text{odd}})$. While integer-rank irregular states admit a well-established free-field construction, the half-integer case is more subtle due to the presence of branch cuts. In this note, we present two equivalent constructions of half-integer irregular representations. The first one is based on a $\mathbb{Z}_2$-twisted free boson, which is motivated from the monodromy structure of Hitchin system. The second one employs a recursion relation of the Virasoro eigenvalues recently proposed in the literature. We explicitly demonstrate the equivalence of these two parameterization schemes at rank $3/2$ and $5/2$. Our analysis clarifies the structure of half-integer irregular modules and provides tools for computing the corresponding irregular states relevant for Argyres-Douglas theories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_11628 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on half-integer irregular representations of Virasoro algebra Zang, Yichi High Energy Physics - Theory We study irregular representations of Virasoro algebra associated with half-integer order singularities, which arise naturally in the 2d CFT description of Argyres-Douglas theories of type $(A_1, A_{\text{even}})$ and $(A_1, D_{\text{odd}})$. While integer-rank irregular states admit a well-established free-field construction, the half-integer case is more subtle due to the presence of branch cuts. In this note, we present two equivalent constructions of half-integer irregular representations. The first one is based on a $\mathbb{Z}_2$-twisted free boson, which is motivated from the monodromy structure of Hitchin system. The second one employs a recursion relation of the Virasoro eigenvalues recently proposed in the literature. We explicitly demonstrate the equivalence of these two parameterization schemes at rank $3/2$ and $5/2$. Our analysis clarifies the structure of half-integer irregular modules and provides tools for computing the corresponding irregular states relevant for Argyres-Douglas theories. |
| title | A note on half-integer irregular representations of Virasoro algebra |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2512.11628 |