Emergent AdS_d+1 Geometry from Functional Renormalization Group via Bulk Metric Reconstruction

2026/05/31 by Hyeon Jung Kim, Ki-Seok Kim
#hep-th

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Abstract

We present a holographic dual description for the O(N) vector model in d-dimensional Euclidean space within the functional renormalization group (FRG) framework. By iterating Wilsonian renormalization group transformations, the extra-dimensional scale coordinate is identified as the radial direction of an emergent (d+1)-dimensional bulk spacetime. We construct a bidirectional holographic dictionary in which the emergent bulk metric is determined by the spectrum of the non-perturbative GG polarization function. Using this dictionary we show that as the mass gap decreases, the emergent geometry evolves from a Ricci flat to an Anti-de Sitter (AdS_d+1) geometry.

Citations

• Dual holography as functional renormalization group
• It from ETH: Multi-interval Entanglement and Replica Wormholes from Large-c BCFT Ensemble
• Gravitational dynamics from collective field theory
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• An emergent geometric description for a topological phase transition in the Kitaev superconductor model
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• Large N Field Theories, String Theory and Gravity
• The Large-N Limit of Superconformal Field Theories and Supergravity
• Exact evolution equation for the effective potential
• Quantum critical phenomena
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Related

• Aspects of the map from Exact RG to Holographic RG in AdS and dS
• Learning geometries beyond asymptotic AdS
• Quantum Renormalization Group and Holography
• Comparison between renormalization group derived emergent dual holography and string theory based holographic duality
• AdS/CFT correspondence and Geometry