di-Langlands correspondence and extended observables
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910770886868992 |
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| author | Jeong, Saebyeok Lee, Norton Nekrasov, Nikita |
| author_facet | Jeong, Saebyeok Lee, Norton Nekrasov, Nikita |
| contents | We explore the $\textit{difference Langlands correspondence}$ using the four dimensional ${\mathcal{N}}=2$ super-QCD. Surface defects and surface observables play the crucial role. As an application, we give the first construction of the full set of quantum integrals, i.e. commuting differential operators, such that the partition function of the so-called regular monodromy surface defect is their joint eigenvectors in an evaluation module over the Yangian $Y(\mathfrak{gl}(2))$, making it the wavefunction of a $N$-site $\mathfrak{gl}(2)$ spin chain with bi-infinite spin modules. We construct the $\mathbf{Q}$- and $\tilde{\mathbf{Q}}$-surface observables which are believed to be the $Q$-operators on the bi-infinite module over the Yangian $Y(\mathfrak{gl}(2))$, and compute their eigenvalues, the $Q$-functions, as vevs of the surface observables. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_13888 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | di-Langlands correspondence and extended observables Jeong, Saebyeok Lee, Norton Nekrasov, Nikita High Energy Physics - Theory Mathematical Physics Differential Geometry Quantum Algebra Exactly Solvable and Integrable Systems We explore the $\textit{difference Langlands correspondence}$ using the four dimensional ${\mathcal{N}}=2$ super-QCD. Surface defects and surface observables play the crucial role. As an application, we give the first construction of the full set of quantum integrals, i.e. commuting differential operators, such that the partition function of the so-called regular monodromy surface defect is their joint eigenvectors in an evaluation module over the Yangian $Y(\mathfrak{gl}(2))$, making it the wavefunction of a $N$-site $\mathfrak{gl}(2)$ spin chain with bi-infinite spin modules. We construct the $\mathbf{Q}$- and $\tilde{\mathbf{Q}}$-surface observables which are believed to be the $Q$-operators on the bi-infinite module over the Yangian $Y(\mathfrak{gl}(2))$, and compute their eigenvalues, the $Q$-functions, as vevs of the surface observables. |
| title | di-Langlands correspondence and extended observables |
| topic | High Energy Physics - Theory Mathematical Physics Differential Geometry Quantum Algebra Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2402.13888 |