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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.16929 |
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| _version_ | 1866910910216404992 |
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| author | Gukov, Sergei Haghighat, Babak Liu, Yihua Reshetikhin, Nicolai |
| author_facet | Gukov, Sergei Haghighat, Babak Liu, Yihua Reshetikhin, Nicolai |
| contents | In this paper we construct irregular representations of the affine Kac-Moody algebra $\widehat{sl}(2,\mathbb{C})$. We show how such irregular representations correspond to irregular Gaiotto-Teschner representations of the Virasoro algebra. The intertwiners for such representations satisfy a version of Knizhnik-Zamolodchikov (KZ) equations which we call irregular KZ equations. By connecting to 2d Liouville theory, we show how the conformal blocks governed by our irregular KZ equation correspond to 4d Argyres-Douglas theories with surface operator insertions. The corresponding flat connections describe braiding between such operators on the Gaiotto curve. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_16929 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Irregular KZ equations and Kac-Moody representations Gukov, Sergei Haghighat, Babak Liu, Yihua Reshetikhin, Nicolai High Energy Physics - Theory In this paper we construct irregular representations of the affine Kac-Moody algebra $\widehat{sl}(2,\mathbb{C})$. We show how such irregular representations correspond to irregular Gaiotto-Teschner representations of the Virasoro algebra. The intertwiners for such representations satisfy a version of Knizhnik-Zamolodchikov (KZ) equations which we call irregular KZ equations. By connecting to 2d Liouville theory, we show how the conformal blocks governed by our irregular KZ equation correspond to 4d Argyres-Douglas theories with surface operator insertions. The corresponding flat connections describe braiding between such operators on the Gaiotto curve. |
| title | Irregular KZ equations and Kac-Moody representations |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2412.16929 |