Quantum spin systems and supersymmetric gauge theories. Part I
Quantum spin systems and supersymmetric gauge theories. Part I
复制标题
量子自旋系统和超对称规范理论。
DOI：
--
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发表时间：
2020
影响因子：
5.4
通讯作者：
N. Nekrasov
中科院分区：
文献类型：
--
作者：
Norton Lee;N. Nekrasov
The relation between supersymmetric gauge theories in four dimensions and quantum spin systems is exploited to find an explicit formula for the Jost function of the N site sl\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathfrak{sl} $$\end{document}2X X X spin chain (for infinite dimensional complex spin representations), as well as the SLN Gaudin system, which reduces, in a limiting case, to that of the N-particle periodic Toda chain. Using the non-perturbative Dyson-Schwinger equations of the supersymmetric gauge theory we establish relations between the spin chain commuting Hamiltonians with the twisted chiral ring of gauge theory. Along the way we explore the chamber dependence of the supersymmetric partition function, also the expectation value of the surface defects, giving new evidence for the AGT conjecture.
The relation between supersymmetric gauge theories in four dimensions and quantum spin systems is exploited to find an explicit formula for the Jost function of the N site sl\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathfrak{sl} $$\end{document}2X X X spin chain (for infinite dimensional complex spin representations), as well as the SLN Gaudin system, which reduces, in a limiting case, to that of the N-particle periodic Toda chain. Using the non-perturbative Dyson-Schwinger equations of the supersymmetric gauge theory we establish relations between the spin chain commuting Hamiltonians with the twisted chiral ring of gauge theory. Along the way we explore the chamber dependence of the supersymmetric partition function, also the expectation value of the surface defects, giving new evidence for the AGT conjecture.