  Superconductivity is abundant near quantum-critical points, where
fluctuations suppress the formation of Fermi liquid quasiparticles and the BCS
theory no longer applies. Two very distinct approaches have been developed to
address this issue: quantum-critical Eliashberg theory and holographic
superconductivity. The former includes a strongly retarded pairing interaction
of ill-defined fermions, the latter is rooted in the duality of quantum field
theory and gravity theory. We demonstrate that both are different perspectives
of the same theory. We derive holographic superconductivity in form of a
gravity theory with emergent space-time from a quantum many-body Hamiltonian -
the Yukawa SYK model - where the Eliashberg formalism is exact. Exploiting the
power of holography, we then determine the dynamic pairing susceptibility of
the model. Our holographic map comes with the potential to use quantum gravity
corrections to go beyond the Eliashberg regime.
