\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 ... View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2011-08

AUTHORS

Yuji Terashima, Masahito Yamazaki

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

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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