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

Abstract

We prove that the \textit{minimal null string theory} on background manifold ${\cal M}$ is classically equivalent to the ILST theory on the projective boundary of $\mathcal M$, ${\mathcal B}_{_{\text{P}}}={\partial_{_{\text{P}}}\mathcal{M}}$. We conjecture that this equivalence also holds as quantum level, which we dub \textit{null string holography}. In particular, we show classical null string theory on Poincar\'e 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 ${\cal I}^\pm$ and timelike infinities $\iota^\pm$. We comment on physical implications of the null string holography on black hole backgrounds whose projective boundary includes horizons.