Quivers, YBE and 3-manifolds

A bstract We study 4d superconformal indices for a large class of superconformal quiver gauge theories realized combinatorially as a bipartite graph or a set of “zig-zag paths” on a two-dimensional torus T 2 . An exchange of loops, which we call a “double Yang-Baxter move”, gives the Seiberg duality...

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Bibliographic Details
Published inThe journal of high energy physics Vol. 2012; no. 5
Main Author Yamazaki, Masahito
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer-Verlag 01.05.2012
Springer Nature B.V
Subjects
Classical and Quantum Gravitation
Elementary Particles
Gauge theory
Gluing
Graph theory
High energy physics
Integrals
Manifolds (mathematics)
Partitions (mathematics)
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Relativity Theory
Saddle points
String Theory
Toruses
Field Theories in Lower Dimensions
Lattice Integrable Models
Supersymmetry and Duality
Supersymmetric gauge theory
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Summary:A bstract We study 4d superconformal indices for a large class of superconformal quiver gauge theories realized combinatorially as a bipartite graph or a set of “zig-zag paths” on a two-dimensional torus T 2 . 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 T 2 . 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 , 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].
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP05(2012)147