di-Langlands correspondence and extended observables

Fuente: arXiv
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Main Authors: Jeong, Saebyeok, Lee, Norton, Nekrasov, Nikita
Format: Preprint
Published: 2024
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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