Quivers, YBE and 3-manifolds View Full Text


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Article Info

DATE

2012-05

AUTHORS

Masahito Yamazaki

ABSTRACT

We study 4d superconformal indices for a large class of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathcal{N} = 1 $\end{document} superconformal quiver gauge theories realized combinatorially as a bipartite graph or a set of “zig-zag paths” on a two-dimensional torus T2. An exchange of loops, which we call a “double Yang-Baxter move”, gives the Seiberg duality of the gauge theory, and the invariance of the index under the duality is translated into the Yang-Baxter-type equation of a spin system defined on a “Z-invariant” lattice on T2. When we compactify the gauge theory to 3d, Higgs the theory and then compactify further to 2d, the superconformal index reduces to an integral of quantum/classical dilogarithm functions. The saddle point of this integral unexpectedly reproduces the hyperbolic volume of a hyperbolic 3-manifold. The 3-manifold is obtained by gluing hyperbolic ideal polyhedra in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ {\mathbb{H}^3} $\end{document}, each of which could be thought of as a 3d lift of the faces of the 2d bipartite graph. The same quantity is also related with the thermodynamic limit of the BPS partition function, or equivalently the genus 0 topological string partition function, on a toric Calabi-Yau manifold dual to quiver gauge theories. We also comment on brane realization of our theories. This paper is a companion to another paper summarizing the results [1]. More... »

PAGES

147

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  • Journal

    TITLE

    Journal of High Energy Physics

    ISSUE

    5

    VOLUME

    2012

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/jhep05(2012)147

    DOI

    http://dx.doi.org/10.1007/jhep05(2012)147

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1043250781


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