Hyperinvariant Spin Network States -- An AdS/CFT Model from First Principles

• URL: http://arxiv.org/abs/2510.06602v1
• Date: Wed, 08 Oct 2025 03:23:38 GMT
• Title: Hyperinvariant Spin Network States -- An AdS/CFT Model from First Principles
• Authors: Fynn Otto, Refik Mansuroglu, Norbert Schuch, Otfried Gühne, Hanno Sahlmann,
• Abstract summary: We study the existence and limitations for hyperinvariant tensor networks incorporating a local SU(2) symmetry.<n>We show that important aspects of the AdS/CFT correspondence are realized in certain quantum states of the gravitational field in LQG.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the existence and limitations for hyperinvariant tensor networks incorporating a local SU(2) symmetry. As discrete implementations of the anti de-Sitter/conformal field theory (AdS/CFT) correspondence, such networks have created bridges between the fields of quantum information theory and quantum gravity. Adding SU(2) symmetry to the tensor network allows a direct connection to spin network states, a basis of the kinematic Hilbert space of loop quantum gravity (LQG). We consider a particular situation where the states can be interpreted as kinematic quantum states for three-dimensional quantum gravity. We show that important aspects of the AdS/CFT correspondence are realized in certain quantum states of the gravitational field in LQG, thus justifying, from first principles, a class of models introduced by [F. Pastawski et al., JHEP 06, 149 (2015)]. We provide examples of hyperinvariant tensor networks, but also prove constraints on their existence in the form of no-go theorems that exclude absolutely maximally entangled states as well as general holographic codes from local SU(2)-invariance. We calculate surface areas as expectation values of the LQG area operator and discuss further possible constraints as a consequence of a decay of correlations on the boundary.

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