Elliptic Stable Envelopes for Certain Non-Symplectic Varieties and Dynamical -Matrices for Superspin Chains from the Bethe/Gauge Correspondence

• Опубліковано в: : Symmetry, Integrability and Geometry: Methods and Applications
• Дата: 2024
• Автори: Ishtiaque, Nafiz, Moosavian, Seyed Faroogh, Zhou, Yehao
• Формат: Стаття
• Мова: Англійська
• Опубліковано: Інститут математики НАН України 2024
• Онлайн доступ: https://nasplib.isofts.kiev.ua/handle/123456789/212645
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Цитувати: Elliptic Stable Envelopes for Certain Non-Symplectic Varieties and Dynamical -Matrices for Superspin Chains from the Bethe/Gauge Correspondence. Nafiz Ishtiaque, Seyed Faroogh Moosavian and Yehao Zhou. SIGMA 20 (2024), 099, 95 pages

We generalize Aganagic-Okounkov's theory of elliptic stable envelopes, and its physical realization in Dedushenko-Nekrasov's and Bullimore-Zhang's works, to certain varieties without holomorphic symplectic structure or polarization. These classes of varieties include, in particular, classical Higgs branches of 3d = 2 quiver gauge theories. The Bethe/gauge correspondence relates such a gauge theory to an isotropic/elliptic superspin chain, and the stable envelopes compute the -matrix that solves the dynamical Yang-Baxter equation (dYBE) for this spin chain. As an illustrative example, we solve the dYBE for the elliptic (1|1) spin chain with fundamental representations using the corresponding 3d = 2 SQCD whose classical Higgs branch is the Lascoux resolution of a determinantal variety. Certain Janus partition functions of this theory on × for an interval and an elliptic curve compute the elliptic stable envelopes, and in turn the geometric elliptic -matrix, of the anisotropic (1|1) spin chain. Furthermore, we consider the 2d and 1d reductions of elliptic stable envelopes and the -matrix. The reduction to 2d gives the K-theoretic stable envelopes, and the trigonometric -matrix, and a further reduction to 1d produces the cohomological stable envelopes and the rational -matrix. The latter recovers Rimányi-Rozansky's results that appeared recently in the mathematical literature.