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

Abstract

We prove that the \textit{minimal null string theory} on a background manifold $\mathcal{M}$ 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 at quantum level, we dub this correspondence \textit{null string holography}. In particular, we show the minimal null string theory on the Poincaré patch of a $D$ dimensional Anti de Sitter (AdS${}_D$) background is described by the ILST theory on $(D-1)$-dimensional Minkowski background, paralleling the celebrated AdS/CFT. The minimal null string theory on the cosmological patch of dS${}_D$ is governed by the ILST theory on $(D-1)$-dimensional flat Euclidean space. For null strings on a $D$-dimensional Minkowski space ${\mathbb{M}}_D$, depending on the coordinate patches used to span ${\mathbb{M}}_D$, the projective boundary includes a dS${}_{D-1}$, asymptotic null infinities ${\mathcal{I}}^{\pm }$ and the hyperboloid ${\mathbb{H}}^{D-1}$ patches. The ILST theory dual to the minimal null strings on each patch, then resides on the piece of the projective boundary spanned by the coordinates adopted in the patch. We comment on possible applications of null string holography to black hole horizons.

14 pages; minor corrections; references added