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arXiv · 2510.06602

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

Fynn Otto·Refik Mansuroglu·Norbert Schuch·Otfried Gühne·Hanno Sahlmann
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Abstract

We study the existence and limitations of 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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Fynn Otto, Refik Mansuroglu, Norbert Schuch, Otfried Gühne, Hanno Sahlmann. 2025-10-08. Hyperinvariant Spin Network States -- An AdS/CFT Model from First Principles. https://doi.org/10.1007/jhep06(2026)145

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