Non-Riemannian Holography: Long Strings and Soft Hair

We propose an $\mathbf{O}(D,D)$-covariant holographic dictionary for two bulk completions of the Gomis–Ooguri boundary data: Riemannian $Ad{S}_3$ supported by pure NS–NS flux and an everywhere non-Riemannian string Newton–Cartan geometry. An $\mathbf{O}(D,D)$-covariant Codazzi identity yields the boundary conservation law. Both branches share diagonal generalized-metric one-point functions, but only the non-Riemannian branch carries independent normalizable soft hair that couples to long strings without contributing to surface charges or the renormalized on-shell action. Supersymmetric non-Riemannian saddles admit arbitrary chiral Killing-spinor profiles, realizing “supersupersymmetry.”