Class $\mathcal{S}$ on $S^2$
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916256405258240 |
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| author | Nawata, Satoshi Pan, Yiwen Zheng, Jiahao |
| author_facet | Nawata, Satoshi Pan, Yiwen Zheng, Jiahao |
| contents | We study 2d $\mathcal{N}=(0,2)$ and $\mathcal{N}=(0,4)$ theories derived from compactifying class $\mathcal{S}$ theories on $S^2$ with a topological twist. We present concise expressions for the elliptic genera of both classes of theories, revealing the TQFT structure on Riemann surfaces $C_{g,n}$. Furthermore, our study highlights the relationship between the left-moving sector of the (0,2) theory and the chiral algebra of the 4d $\mathcal{N}=2$ theory. Notably, we propose that the (0,2) elliptic genus of a theory of this class can be expressed as a linear combination of characters of the corresponding chiral algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_07965 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Class $\mathcal{S}$ on $S^2$ Nawata, Satoshi Pan, Yiwen Zheng, Jiahao High Energy Physics - Theory Mathematical Physics We study 2d $\mathcal{N}=(0,2)$ and $\mathcal{N}=(0,4)$ theories derived from compactifying class $\mathcal{S}$ theories on $S^2$ with a topological twist. We present concise expressions for the elliptic genera of both classes of theories, revealing the TQFT structure on Riemann surfaces $C_{g,n}$. Furthermore, our study highlights the relationship between the left-moving sector of the (0,2) theory and the chiral algebra of the 4d $\mathcal{N}=2$ theory. Notably, we propose that the (0,2) elliptic genus of a theory of this class can be expressed as a linear combination of characters of the corresponding chiral algebra. |
| title | Class $\mathcal{S}$ on $S^2$ |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2310.07965 |