Quantum Flat Connections, KZ equations, and Integrability
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910262897934336 |
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| author | Banerjee, Sibasish Haghighat, Babak Latifi, Anouchah |
| author_facet | Banerjee, Sibasish Haghighat, Babak Latifi, Anouchah |
| contents | N=2 supersymmetric Yang-Mills theories are described in terms of a Hitchin system over a Riemann surface C. Focusing on strongly coupled Argyres-Douglas theories, we show that the corresponding flat bundle over C can be quantized such that the resulting quantum flat connection is integrable. For $sl_2$, the quantum connection takes values in $gl_2$(A) where A is an associative algebra which we explicitly describe for the cases of Painlevé I, II and IV. Moreover, we find that the quantum connection is equivalent to irregular versions of Knizhnik-Zamolodchikov (KZ) connections. Utilizing a suitable gauge transformation, one can show that the corresponding KZ equations give rise to BPZ equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_26159 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantum Flat Connections, KZ equations, and Integrability Banerjee, Sibasish Haghighat, Babak Latifi, Anouchah High Energy Physics - Theory Representation Theory N=2 supersymmetric Yang-Mills theories are described in terms of a Hitchin system over a Riemann surface C. Focusing on strongly coupled Argyres-Douglas theories, we show that the corresponding flat bundle over C can be quantized such that the resulting quantum flat connection is integrable. For $sl_2$, the quantum connection takes values in $gl_2$(A) where A is an associative algebra which we explicitly describe for the cases of Painlevé I, II and IV. Moreover, we find that the quantum connection is equivalent to irregular versions of Knizhnik-Zamolodchikov (KZ) connections. Utilizing a suitable gauge transformation, one can show that the corresponding KZ equations give rise to BPZ equations. |
| title | Quantum Flat Connections, KZ equations, and Integrability |
| topic | High Energy Physics - Theory Representation Theory |
| url | https://arxiv.org/abs/2604.26159 |