Emergent 3-manifolds from 4d 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 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.

arXiv commentv2: 4 pages, 2 figures, explanations added, published in PRL

References in corpus (21)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• An Index for 4 dimensional Super Conformal Theories
• Counting chiral primaries in N=1 d=4 superconformal field theories
• SUSY Gauge Theories on Squashed Three-Spheres
• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• Brane Dimers and Quiver Gauge Theories
• The 4d Superconformal Index from q-deformed 2d Yang-Mills
• S-duality and 2d Topological QFT
• SL(2,R) Chern-Simons, Liouville, and Gauge Theory on Duality Walls
• From 4d superconformal indices to 3d partition functions
• Quivers, Tilings, Branes and Rhombi
• Elliptic hypergeometry of supersymmetric dualities
• Abelian Current Algebra and the Virasoro Algebra on the Lattice
• Brane Tilings and Their Applications
• Relation between the 4d superconformal index and the S^3 partition function
• Faddeev-Volkov solution of the Yang-Baxter Equation and Discrete Conformal Symmetry
• On the Superconformal Index of N=1 IR Fixed Points: A Holographic Check
• Quivers, YBE and 3-manifolds
• Elliptic gamma-function and multi-spin solutions of the Yang-Baxter equation
• Exactly marginal deformations of quiver gauge theories as seen from brane tilings
• Global symmetries and 't Hooft anomalies in brane tilings

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• New Integrable Models from the Gauge/YBE Correspondence
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• Comment on star-star relations in statistical mechanics and elliptic gamma-function identities
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• Entanglement in Theory Space
• A New Integrable Ising-type Model from 2d $\mathcal{N}$=(2,2) Dualities
• Mahler Measure for a Quiver Symphony
• Cluster-Enriched Yang-Baxter Equation from SUSY Gauge Theories
• Integrability As Duality: The Gauge/YBE Correspondence
• Lens Generalisation of $\tau$-functions for the Elliptic Discrete Painlevé Equation
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