Hyperinvariant Spin Network States -- An AdS/CFT Model from First Principles
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915538744115200 |
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| author | Otto, Fynn Mansuroglu, Refik Schuch, Norbert Gühne, Otfried Sahlmann, Hanno |
| author_facet | Otto, Fynn Mansuroglu, Refik Schuch, Norbert Gühne, Otfried Sahlmann, Hanno |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_06602 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hyperinvariant Spin Network States -- An AdS/CFT Model from First Principles Otto, Fynn Mansuroglu, Refik Schuch, Norbert Gühne, Otfried Sahlmann, Hanno Quantum Physics General Relativity and Quantum Cosmology High Energy Physics - Theory 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. |
| title | Hyperinvariant Spin Network States -- An AdS/CFT Model from First Principles |
| topic | Quantum Physics General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2510.06602 |