Speaker: Ding Xiangmao, professor, Academy of Mathematics and Systems Science, CAS

Date: November 22, 2024

Time: 10:30-11:30 am

Location: B1032,Zhixin Building, Shandong University

Sponsor: School of Mathematics, Shandong University

Abstract:

Nekrasov proposed aΩ-deformation of the Seiberg-Witten theory with two parametersε1 andε2. Ifε1=ε2 = 0, the supersymmetry gauge theory reappears the Seiberg-Witten as its classical limit. Ifε1 = h andε2 = 0, this algebraic classical correspondence is nicely to quantum integrable model correspondence by the NS limit. The first non-trivial realization of this kind of duality is XXZ spin chain/N=2 3d Gauge theory with A-type gauge group. The first non-trivial realization of this kind of duality is by Nekrasov, that XXZ spin chain duality with N=2 3d Gauge theory with A-type gauge group. We reconsider the effective super potentials for supersymmetric gauge theory with roots of Lie algebras and encoding a fusion parameter μ. For 3d (or 2d) supersymmetry gauge theory with a simpler representation, we find that μ = 2 is naively to get correspondence to closed and open XXZ (or XXX) spin chain. For a sense, μ= 1 is being as a special case, and we have just been using the get the right Bethe/Gauge correspondence. The degenerate case of μ= 0 can fit the XX model reduced from the XXZ spin chain, which is never mentioned before. In mathematical, ADE are self-dual, for non-simple laced Lie algebras, the B_N and C_N are Langlands dual to each other. Specifically, for the ADE-type Lie algebras, the effective super potentials are self-dual for the two realizations. For the non-simple laced Lie algebras B_N and C_N, their roles are exchanged in the two realizations, compared with the results in the μ =1 case, in which the two kinds of the effective super potentials are Langlands duality to μ = 2 case each other. For the B_N-type Lie algebra, a remarkable feature is that to fix the spin sites parameters by boundaries through Bethe/Gauge, the spins of the sites will be reversed, we call this as a boundary-spin effect, a new kind of duality.

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https://www.view.sdu.edu.cn/info/1020/197262.htm