Holographic duality from a four-fermion interaction: emergent AdS$_3$/CFT$_2$, D-branes, and Einstein gravity

Abstract

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.