Superintegrability for some $(q,t)$-deformed matrix models
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910227190775808 |
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| author | Liu, Fan Wang, Rui Yang, Jie Zhao, Wei-Zhong |
| author_facet | Liu, Fan Wang, Rui Yang, Jie Zhao, Wei-Zhong |
| contents | We analyze the Macdonald's $(q,t)$-deformed hypergeometric functions with one and two set variables and present their constraints. We prove the uniqueness to the solutions of these constraints. We propose a concise method to prove the superintegrability relations for $(q,t)$-deformed matrix models, where the constraints of hypergeometric functions play a crucial role. A conjectured superintegrability relation in the literature for the refined Chern-Simons model can be easily proved by our method. Moreover, we construct a general $(q,t)$-deformed matrix model. We give the constraint conditions for parameters in the integral. The superintegrability relations for the $(q,t)$-deformed integrals with allowed parameters are derived from the hypergeometric constraints. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_18524 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Superintegrability for some $(q,t)$-deformed matrix models Liu, Fan Wang, Rui Yang, Jie Zhao, Wei-Zhong High Energy Physics - Theory Mathematical Physics We analyze the Macdonald's $(q,t)$-deformed hypergeometric functions with one and two set variables and present their constraints. We prove the uniqueness to the solutions of these constraints. We propose a concise method to prove the superintegrability relations for $(q,t)$-deformed matrix models, where the constraints of hypergeometric functions play a crucial role. A conjectured superintegrability relation in the literature for the refined Chern-Simons model can be easily proved by our method. Moreover, we construct a general $(q,t)$-deformed matrix model. We give the constraint conditions for parameters in the integral. The superintegrability relations for the $(q,t)$-deformed integrals with allowed parameters are derived from the hypergeometric constraints. |
| title | Superintegrability for some $(q,t)$-deformed matrix models |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2510.18524 |