Classical and quantum curves of 5d Seiberg's theories and their 4d limit
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915003757494272 |
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| author | Chalykh, Oleg Lü, Yongchao |
| author_facet | Chalykh, Oleg Lü, Yongchao |
| contents | In this work, we examine the classical and quantum Seiberg-Witten curves of 5d N = 1 SCFTs and their 4d limits. The 5d theories we consider are Seiberg's theories of type $E_{6,7,8}$, which serve as the UV completions of 5d SU(2) gauge theories with 5, 6, or 7 flavors. Their classical curves can be constructed using the five-brane web construction [1]. We also use it to re-derive their quantum curves [2], by employing a q-analogue of the Frobenius method in the style of [3]. This allows us to compare the reduction of these 5d curves with the 4d curves, i.e. Seiberg-Witten curves of the Minahan-Nemeschansky theories and their quantization, which have been identified in [4] with the spectral curves of rank-1 complex crystallographic elliptic Calogero-Moser systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_01802 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classical and quantum curves of 5d Seiberg's theories and their 4d limit Chalykh, Oleg Lü, Yongchao High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems In this work, we examine the classical and quantum Seiberg-Witten curves of 5d N = 1 SCFTs and their 4d limits. The 5d theories we consider are Seiberg's theories of type $E_{6,7,8}$, which serve as the UV completions of 5d SU(2) gauge theories with 5, 6, or 7 flavors. Their classical curves can be constructed using the five-brane web construction [1]. We also use it to re-derive their quantum curves [2], by employing a q-analogue of the Frobenius method in the style of [3]. This allows us to compare the reduction of these 5d curves with the 4d curves, i.e. Seiberg-Witten curves of the Minahan-Nemeschansky theories and their quantization, which have been identified in [4] with the spectral curves of rank-1 complex crystallographic elliptic Calogero-Moser systems. |
| title | Classical and quantum curves of 5d Seiberg's theories and their 4d limit |
| topic | High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2411.01802 |