Ontology type: schema:ScholarlyArticle Open Access: True
2015-11-18
AUTHORSMichele Del Zotto, Cumrun Vafa, Dan Xie
ABSTRACTWe study compactification of 6 dimensional (1,0) theories on T2. We use geometric engineering of these theories via F-theory and employ mirror symmetry technology to solve for the effective 4d N=2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N}=2 $$\end{document} geometry for a large number of the (1,0) theories including those associated with conformal matter. Using this we show that for a given 6d theory we can obtain many inequivalent 4d N=2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N}=2 $$\end{document} SCFTs. Some of these respect the global symmetries of the 6d theory while others exhibit SL(2, ℤ) duality symmetry inherited from global diffeomorphisms of the T2. This construction also explains the 6d origin of moduli space of 4d affine ADE quiver theories as flat ADE connections on T2. Among the resulting 4dN=2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N}=2 $$\end{document} CFTs we find theories whose vacuum geometry is captured by an LG theory (as opposed to a curve or a local CY geometry). We obtain arbitrary genus curves of class S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{S} $$\end{document} with punctures from toroidal compactification of (1, 0) SCFTs where the curve of the class S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{S} $$\end{document} theory emerges through mirror symmetry. We also show that toroidal compactification of the little string version of these theories can lead to class S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{S} $$\end{document} theories with no punctures on arbitrary genus Riemann surface. More... »
PAGES123
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DOIhttp://dx.doi.org/10.1007/jhep11(2015)123
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