Quantum Spectral Curve for a cusped Wilson line in N=4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N}=4 $$\end{document} SYM

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作者
Nikolay Gromov
Fedor Levkovich-Maslyuk
机构
[1] King’s College London,
[2] Department of Mathematics,undefined
[3] St. Petersburg INP,undefined
关键词
AdS-CFT Correspondence; Integrable Field Theories;
D O I
10.1007/JHEP04(2016)134
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学科分类号
摘要
We show that the Quantum Spectral Curve (QSC) formalism, initially formulated for the spectrum of anomalous dimensions of all local single trace operators in N=4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N}=4 $$\end{document} SYM, can be extended to the generalized cusp anomalous dimension for all values of the parameters. We find that the large spectral parameter asymptotics and some analyticity properties have to be modified, but the functional relations are unchanged. As a demonstration, we find an all-loop analytic expression for the first two nontrivial terms in the small |ϕ ± θ| expansion. We also present nonperturbative numerical results at generic angles which match perfectly 4-loop perturbation theory and the classical string prediction.
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