Null String Holography, Null Strings Probe Projective Boundary of Their Target Spaces

We prove that the $\mathit{\text{minimal}}\mathit{\text{null}}\mathit{\text{string}}\mathit{\text{theory}}$ on background manifold $\mathcal{M}$ is classically equivalent to the ILST theory on the projective boundary of $\mathcal{M}$, ${\mathcal{B}}_{{}_{\text{P}}}={\mathrm{\partial }}_{{}_{\text{P}}}\mathcal{M}$. We conjecture that this equivalence also holds as quantum level, which we dub $\mathit{\text{null}}\mathit{\text{string}}\mathit{\text{holography}}$. In particular, we show classical null string theory on Poincaré patch of $D$ dimensional Anti de Sitter (AdS${}_D$) background is described by ILST on $D-1$ dimensional Minkowski background, paralleling the celebrated AdS/CFT. Null strings on cosmological patch of dS${}_D$ is governed by ILST on $D-1$ dimensional flat Euclidean space. For null strings on $D$ dimensional Minkowski space, depending on the coordinate patch used, the projective boundary where the ``dual’’ ILST theory resides, can by dS${}_{D-1}$, $D-1$ dimensional Carrollian space and $D-1$ dimensional hyperboloid, respectively including spacelike asymptotic boundary ${\iota }^0$, asymptotic null boundaries ${\mathcal{I}}^{\pm }$ and timelike infinities ${\iota }^{\pm }$. We comment on physical implications of the null string holography on black hole backgrounds whose projective boundary includes horizons.