TY - JOUR

T1 - Emergent 3-manifolds from four dimensional superconformal indices

AU - Terashima, Yuji

AU - Yamazaki, Masahito

PY - 2012/8/28

Y1 - 2012/8/28

N2 - 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 T2 and (2) the partition function of a classical integrable spin chain on T2. 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.

AB - 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 T2 and (2) the partition function of a classical integrable spin chain on T2. 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.

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U2 - 10.1103/PhysRevLett.109.091602

DO - 10.1103/PhysRevLett.109.091602

M3 - Article

AN - SCOPUS:84865589592

VL - 109

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 9

M1 - 091602

ER -