title: Emergent 3-manifolds from four dimensional superconformal indices.
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 (2) 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 using the Higgs mechanism in the 4D gauge theory.
authors.affiliation: Department of Mathematics, Tokyo Institute for Technology, Tokyo, Japan.
authors.forename: Yuji
authors.initials: Y
authors.lastname: Terashima
authors.forename: Masahito
authors.initials: M
authors.lastname: Yamazaki