QG from SymQRG: AdS$_3$/CFT$_2$ Correspondence as Topological Symmetry-Preserving Quantum RG Flow

Ning Bao; Ling-Yan Hung; Yikun Jiang; Zhihan Liu

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QG from SymQRG: AdS $_3$ /CFT $_2$ Correspondence as Topological Symmetry-Preserving Quantum RG Flow

by Ning Bao, Ling-Yan Hung, Yikun Jiang, Zhihan Liu

Submission summary

Authors (as registered SciPost users):

Yikun Jiang

Submission information
Preprint Link:	https://arxiv.org/abs/2412.12045v2 (pdf)
Date submitted:	2025-03-18 17:07
Submitted by:	Jiang, Yikun
Submitted to:	SciPost Physics

Ontological classification
Academic field:	Physics
Specialties:	High-Energy Physics - Theory Mathematical Physics
Approach:	Theoretical

Abstract

By analyzing the non-perturbative RG flows that explicitly preserve given symmetries, we demonstrate that they can be expressed as quantum path integrals of the $\textit{SymTFT}$ in one higher dimension. When the symmetries involved include Virasoro defect lines, such as in the case of $T\bar{T}$ deformations, the RG flow corresponds to the 3D quantum gravitational path integral. For each 2D CFT, we identify a corresponding ground state of the SymTFT, from which the Wheeler-DeWitt equation naturally emerges as a non-perturbative constraint. These observations are summarized in the slogan: $\textbf{SymQRG = QG}$ . The recently proposed exact discrete formulation of Liouville theory in [1] allows us to identify a universal SymQRG kernel, constructed from quantum $6j$ symbols associated with $U_q(SL(2,\mathbb{R}))$ . This kernel is directly related to the quantum path integral of the Virasoro TQFT, and manifests itself as an exact and analytical 3D background-independent MERA-type holographic tensor network. Many aspects of the AdS/CFT correspondence, including the factorization puzzle, admit a natural interpretation within this framework. This provides the first evidence suggesting that there is a universal holographic principle encompassing AdS/CFT and topological holography. We propose that the non-perturbative AdS/CFT correspondence is a $\textit{maximal}$ form of topological holography.

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Current status:

In refereeing