Holographic duality from a four-fermion interaction: emergent AdS$_3$/CFT$_2$, D-branes, and Einstein gravity
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910210635857920 |
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| author | Haddad, Laith H. |
| author_facet | Haddad, Laith H. |
| contents | We derive the bosonic sector of the AdS$_3$/CFT$_2$ correspondence from the $(1+1)$-dimensional Gross-Neveu (GN) model with $N$ fermion species and a local quartic interaction, with no stringy or geometric input. A Bargmann-Wigner fusion scheme generates an infinite tower of higher-spin composite fields with a linear Regge trajectory. Competition between spin-0 (chiral) condensation and spin-1 pairing defines an emergent radial coordinate; local fluctuations of this condensate ratio, tracked by a comoving derivative, generate the AdS$_3$ line element. The large-$N$ species sum promotes $z$ from a parameter to a genuine bulk dimension. We show that the full $SO(2,2)$ bulk isometry group, whose special conformal generators mix $z$ with the boundary GN coordinates, emerges from local symmetries of the boundary condensates, and holographic RG flow identifies $z$ with the Wilsonian cutoff scale.We find that a hierarchy of phase transitions in the enlarged GN model map to a bulk description: spin-2 decoherence $\to$ spin-1 decoherence $\to$ chiral symmetry restoration occur at the Hawking-Page, Hagedorn, and Planck temperatures in the bulk picture, respectively, represented as a layered radial profile of the bulk geometry, with successive condensate sectors dissolving at progressively greater depths into the bulk. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_27824 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Holographic duality from a four-fermion interaction: emergent AdS$_3$/CFT$_2$, D-branes, and Einstein gravity Haddad, Laith H. High Energy Physics - Theory Other Condensed Matter General Relativity and Quantum Cosmology Mathematical Physics We derive the bosonic sector of the AdS$_3$/CFT$_2$ correspondence from the $(1+1)$-dimensional Gross-Neveu (GN) model with $N$ fermion species and a local quartic interaction, with no stringy or geometric input. A Bargmann-Wigner fusion scheme generates an infinite tower of higher-spin composite fields with a linear Regge trajectory. Competition between spin-0 (chiral) condensation and spin-1 pairing defines an emergent radial coordinate; local fluctuations of this condensate ratio, tracked by a comoving derivative, generate the AdS$_3$ line element. The large-$N$ species sum promotes $z$ from a parameter to a genuine bulk dimension. We show that the full $SO(2,2)$ bulk isometry group, whose special conformal generators mix $z$ with the boundary GN coordinates, emerges from local symmetries of the boundary condensates, and holographic RG flow identifies $z$ with the Wilsonian cutoff scale.We find that a hierarchy of phase transitions in the enlarged GN model map to a bulk description: spin-2 decoherence $\to$ spin-1 decoherence $\to$ chiral symmetry restoration occur at the Hawking-Page, Hagedorn, and Planck temperatures in the bulk picture, respectively, represented as a layered radial profile of the bulk geometry, with successive condensate sectors dissolving at progressively greater depths into the bulk. |
| title | Holographic duality from a four-fermion interaction: emergent AdS$_3$/CFT$_2$, D-branes, and Einstein gravity |
| topic | High Energy Physics - Theory Other Condensed Matter General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2603.27824 |