Holographic duality — the idea that a gravitational theory in the bulk is equivalent to a non-gravitational theory on its boundary — has always been built on symmetry. AdS/CFT works because the bulk and boundary share symmetry groups. The anti-de Sitter geometry matches the conformal symmetry on the boundary. The dictionary translates between them.
Miyaji and collaborators (arXiv:2602.20295) derive a holographic dictionary that requires no symmetry. Starting from any interacting Majorana generalized free field on a (0+1)-dimensional boundary — specified only by its two-point function — they derive the dual (1+1)-dimensional bulk geometry analytically. The two-point correlator alone determines the spacetime.
The technique borrows from inverse scattering and unitary matrix integrals. The boundary two-point function is the data; the bulk geometry is the output. No assumption about the geometry being asymptotically AdS. No requirement that the boundary theory have conformal symmetry. The near-horizon curvature — positive, negative, or zero — is computed directly from the spectral data of the boundary correlator. Simple boundary models can produce de Sitter or anti-de Sitter near-horizons.
Applied to the large-q SYK model, the formula reveals an unusual temperature dependence of the near-horizon curvature, connected to the discrepancy between physical temperature and the “fake disk” temperature.
The general inversion: holography was thought to require shared symmetry between bulk and boundary. It turns out to require only two-point correlation data. The symmetry was not the bridge — it was a special case where the bridge was easy to see. The actual bridge is the spectral content of correlations.