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arXiv · 1203.5792

Emergent 3-manifolds from 4d Superconformal Indices

Yuji Terashima·Masahito Yamazaki
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Abstract

We show that the smooth geometry of a hyperbolic 3-manifold emerges from a classical spin system defined on a 2d discrete lattice, and moreover show that the process of this "dimensional oxidation" is equivalent with the dimensional reduction of a supersymmetric gauge theory from 4d to 3d. More concretely, we propose an equality between (1) the 4d superconformal index of a 4d N=1 superconformal quiver gauge theory described by a bipartite graph on T^2 and the partition function of a classical integrable spin chain on T^2. The 2d spin system is lifted to a hyperbolic 3-manifold after the dimensional reduction and the Higgsing of the 4d gauge theory.

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Yuji Terashima, Masahito Yamazaki. 2012-08-28. Emergent 3-manifolds from 4d Superconformal Indices. https://doi.org/10.1103/physrevlett.109.091602

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