Abstract
We explore the 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 \( \left(\mathfrak{gl}(2)\right) \), making it the wavefunction of a N-site \( \mathfrak{gl}(2) \) spin chain with bi-infinite spin modules. We construct the Q- and \( \overset{\sim }{\textbf{Q}} \)-surface observables which are believed to be the Q-operators on the bi-infinite module over the Yangian Y \( \left(\mathfrak{gl}(2)\right) \), and compute their eigenvalues, the Q-functions, as vevs of the surface observables.
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Acknowledgments
The authors thank Mina Aganagic, Kevin Costello, Mykola Dedushenko, Chris Elliott, Alba Grassi, Nathan Haouzi, Nafiz Ishtiaque, Shota Komatsu, Jihwan Oh, Andrei Okounkov, Miroslav Rapčák, and Yehao Zhou for discussions and collaboration on related subjects. SJ is grateful to Du Pei for helpful discussion and support during his visit to Center for Quantum Mathematics at University of Southern Denmark, where a part of the work was done. The work of SJ is supported by CERN and CKC fellowship. The work of NL is supported by IBS project IBS-R003-D1. Research of NN is partly supported by NSF grant 2310279.
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Dedicated to the 40th anniversary of the BPZ paper [1].
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Jeong, S., Lee, N. & Nekrasov, N. di-Langlands correspondence and extended observables. J. High Energ. Phys. 2024, 105 (2024). https://doi.org/10.1007/JHEP06(2024)105
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DOI: https://doi.org/10.1007/JHEP06(2024)105