Asymptotic Flatness, Little String Theory, and Holography

TL;DR

The paper proposes a holographic dual for asymptotically flat spacetimes that resides at spacelike infinity, realized on a Lorentzian hyperboloid $\mathcal{H}$ and closely related to de Sitter space in $(d-1)$ dimensions. It develops boundary data (via $\alpha(\eta),$ $\beta(\eta)$) and boundary operators on $\mathcal{H}$, and analyzes boundary correlators for bulk scalar fields using both on-shell-action and Wightman-function approaches. The key result is that boundary Wightman functions are finite and well-defined and yield a time-ordered function through a spectral representation, while the on-shell-action method encounters non-local, non-analytic contact terms leading to ambiguities; the comparison with linear dilaton backgrounds (little string theory) reveals similar non-locality and supports the plausibility of a meaningful non-AdS holography. The work suggests a deep connection between boundary correlators on spacelike infinity and bulk S-matrix data, while highlighting open issues on locality, translation symmetry, and the precise role of deformations, motivating further study in more general spacetimes and in string-theoretic realizations.

Abstract

We argue that any non-gravitational holographic dual to asymptotically flat string theory in $d$-dimensions naturally resides at spacelike infinity. Since spacelike infinity can be resovled as a $(d-1)$-dimensional timelike hyperboloid (i.e., as a copy of de Sitter space in $(d-1)$ dimensions), the dual theory is defined on a Lorentz signature spacetime. Conceptual issues regarding such a duality are clarified by comparison with linear dilaton boundary conditions, such as those dual to little string theory. We compute both time-ordered and Wightman boundary 2-point functions of operators dual to massive scalar fields in the asymptotically flat bulk.