Non-Riemannian Holography: Long Strings and Soft Hair

Abstract: We propose an $\mathbf{O}(D,D)$-covariant holographic dictionary for two bulk completions of the Gomis--Ooguri boundary data: Riemannian $AdS_3$ 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."