# \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\text{SL}}\left( {2,\mathbb{R}} \right)$\end{document} Chern-Simons, Liouville, and gauge theory on ...

Ontology type: schema:ScholarlyArticle      Open Access: True

### Article Info

DATE

2011-08

AUTHORS ABSTRACT

We propose an equivalence of the partition functions of two different 3d gauge theories. On one side of the correspondence we consider the partition function of 3d \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\text{SL}}\left( {2,\mathbb{R}} \right)$\end{document} Chern-Simons theory on a 3-manifold, obtained as a punctured Riemann surface times an interval. On the other side we have a partition function of a 3d \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} superconformal field theory on S3, which is realized as a duality domain wall in a 4d gauge theory on S4. We sketch the proof of this conjecture using connections with quantum Liouville theory and quantum Teichmüller theory, and study in detail the example of the once-punctured torus. Motivated by these results we advocate a direct Chern-Simons interpretation of the ingredients of (a generalization of) the Alday-Gaiotto-Tachikawa relation. We also comment on M5-brane realizations as well as on possible generalizations of our proposals. More... »

PAGES

135

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• ### Journal

TITLE

Journal of High Energy Physics

ISSUE

8

VOLUME

2011

### Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/jhep08(2011)135

DOI

http://dx.doi.org/10.1007/jhep08(2011)135

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1046909813

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