Gauge Theory and Integrability: An Overview
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916942658404352 |
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| author | Yamazaki, Masahito |
| author_facet | Yamazaki, Masahito |
| contents | While general quantum field theories (QFTs) have yet to be rigorously defined in mathematics, they have generated new mathematics and have served as a unifying principle connecting different branches of the subject. In 1989, Witten made a profound impact on the mathematical community by systematically constructing knot invariants via the three-dimensional Chern-Simons theory. One of the historical roots of knot invariants was integrable models, whose explanation in terms of QFT remained unsolved for decades. Recently, this problem was solved by a perturbative analysis of the four-dimensional Chern-Simons theory, which provides a novel framework for understanding and unifying many different aspects of integrable models. In this article, we summarize the basic aspects of these developments for non-experts in both physics and mathematics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_07628 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gauge Theory and Integrability: An Overview Yamazaki, Masahito High Energy Physics - Theory Statistical Mechanics Mathematical Physics Quantum Algebra While general quantum field theories (QFTs) have yet to be rigorously defined in mathematics, they have generated new mathematics and have served as a unifying principle connecting different branches of the subject. In 1989, Witten made a profound impact on the mathematical community by systematically constructing knot invariants via the three-dimensional Chern-Simons theory. One of the historical roots of knot invariants was integrable models, whose explanation in terms of QFT remained unsolved for decades. Recently, this problem was solved by a perturbative analysis of the four-dimensional Chern-Simons theory, which provides a novel framework for understanding and unifying many different aspects of integrable models. In this article, we summarize the basic aspects of these developments for non-experts in both physics and mathematics. |
| title | Gauge Theory and Integrability: An Overview |
| topic | High Energy Physics - Theory Statistical Mechanics Mathematical Physics Quantum Algebra |
| url | https://arxiv.org/abs/2509.07628 |