Gauge/Bethe correspondence from quiver BPS algebras

D Galakhov, W Li, M Yamazaki - Journal of High Energy Physics, 2022 - Springer
A bstract We study the Gauge/Bethe correspondence for two-dimensional\(\mathcal {N}\)=(2,
2) supersymmetric quiver gauge theories associated with toric Calabi-Yau three-folds …

Folded quantum integrable models and deformed W-algebras

E Frenkel, D Hernandez, N Reshetikhin - Letters in Mathematical Physics, 2022 - Springer
We propose a novel quantum integrable model for every non-simply laced simple Lie
algebra g, which we call the folded integrable model. Its spectra correspond to solutions of …

A general framework for the analytic Langlands correspondence

P Etingof, E Frenkel, D Kazhdan - arxiv preprint arxiv:2311.03743, 2023 - arxiv.org
We discuss a general framework for the analytic Langlands correspondence over an
arbitrary local field F introduced and studied in our works arxiv: 1908.09677, arxiv …

Extended Baxter relations and QQ-systems for quantum affine algebras

E Frenkel, D Hernandez - Communications in Mathematical Physics, 2024 - Springer
Generalized Baxter's TQ-relations and the QQ-system are systems of algebraic relations in
the category O of representations of the Borel subalgebra of the quantum affine algebra U q …

di-Langlands correspondence and extended observables

S Jeong, N Lee, N Nekrasov - Journal of High Energy Physics, 2024 - Springer
A bstract We explore the difference Langlands correspondence using the four
dimensional\(\mathcal {N}\)= 2 super-QCD. Surface defects and surface observables play …

Quantum K-theory of quiver varieties and many-body systems

P Koroteev, PP Pushkar, AV Smirnov, AM Zeitlin - Selecta Mathematica, 2021 - Springer
We define quantum equivariant K-theory of Nakajima quiver varieties. We discuss type A in
detail as well as its connections with quantum XXZ spin chains and trigonometric …

QQ-system and Weyl-type transfer matrices in integrable SO (2r) spin chains

G Ferrando, R Frassek, V Kazakov - Journal of High Energy Physics, 2021 - Springer
A bstract We propose the full system of Baxter Q-functions (QQ-system) for the integrable
spin chains with the symmetry of the D r Lie algebra. We use this QQ-system to derive new …

Representations of shifted quantum affine algebras and cluster algebras I: The simply laced case

C Geiss, D Hernandez, B Leclerc - Proceedings of the London …, 2024 - Wiley Online Library
We introduce a family of cluster algebras of infinite rank associated with root systems of type
AA, DD, E E. We show that suitable completions of these cluster algebras are isomorphic to …

A new realization of quantum algebras in gauge theory and Ramification in the Langlands program

N Haouzi - arxiv preprint arxiv:2311.04367, 2023 - arxiv.org
We realize the fundamental representations of quantum algebras via the supersymmetric
Higgs mechanism in gauge theories with 8 supercharges on an $\Omega $-background. We …

Miura operators as R-matrices from M-brane intersections

N Haouzi, S Jeong - arxiv preprint arxiv:2407.15990, 2024 - arxiv.org
We propose that Miura operators are R-matrices of certain infinite-dimensional quantum
algebras. We test our proposal by realizing Miura operators of $ q $-deformed $ W $-and $ Y …