A two-point hologram for everything

A

bstract

Known holographic dictionaries, especially AdS/CFT, rely on symmetry matching between the bulk and the boundary. We take a step toward a holographic dictionary with no symmetry requirement and without assuming the geometry being asymptotically AdS. Starting from almost any interacting Majorana generalized free field on a (0 + 1)d boundary and its two-point function data, we derive a concise analytic formula for the dual (1 + 1)d bulk geometry, borrowing techniques from unitary matrix integral and inverse scattering. Using this formula, we compute the near-horizon curvature, give conditions for positive versus negative curvature, and identify simple boundary models with de Sitter or anti-de Sitter near-horizon duals. We also study the large- q SYK model, finding an unusual temperature dependence of the near-horizon curvature, related to the discrepancy between physical temperature and the “fake disk” temperature. We also construct, directly from boundary operators, approximate algebras generated by null translations and boost that become exact at the bifurcate horizon.