A universal W-algebra for N\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$ \mathcal{N} $$\end{document} = 4 super Yang-Mills

[摘要] Using bootstrap methods, we provide evidence for the existence of a non-linear W-algebra, denoted W∞s,s\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$ {\mathcal{W}}_{\infty}^{\mathrm{s},\mathrm{s}} $$\end{document}, which contains the smallN\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$ \mathcal{N} $$\end{document} = 4 super Virasoro algebra and features an infinite tower of additional generators, organized in short supersymmetry multiplets. The algebra W∞s,s\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$ {\mathcal{W}}_{\infty}^{\mathrm{s},\mathrm{s}} $$\end{document} has one free parameter, its central charge c. We claim that the simple quotient of W∞s,s\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$ {\mathcal{W}}_{\infty}^{\mathrm{s},\mathrm{s}} $$\end{document} for c = –3(N2 – 1) is isomorphic to the vertex operator algebra associated to 4d N\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$ \mathcal{N} $$\end{document} = 4 suN\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$ \mathfrak{su}(N) $$\end{document} super Yang-Mills theory. We define a filtration in W∞s,s\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$ {\mathcal{W}}_{\infty}^{\mathrm{s},\mathrm{s}} $$\end{document} and provide evidence that it reproduces the R-filtration, which is crucial to extract 4d SCFT data from the vertex operator algebra. Finally, we present explicit formulae for all the (anti)commutators of the wedge algebra of W∞s,s\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$ {\mathcal{W}}_{\infty}^{\mathrm{s},\mathrm{s}} $$\end{document}.

[发布日期] 2026-09-02

[关键词] N;Conformal and W Symmetry;Supersymmetric Gauge Theory