Holographic description of asymptotically AdS_2 collapse geometries
David A Lowe, Shubho Roy
TL;DR
This work addresses holographic reconstruction in a time-dependent AdS$_2$ collapse geometry by exploiting boundary analyticity to map local bulk operators to non-local boundary operators with compact support. The authors construct explicit boundary-to-bulk smearing functions for outside-horizon points in both massless and massive cases, deriving Green's functions that respect spacelike boundary support and implementing cross-shell matching across a null shock. Inside the horizon, bulk operators are reconstructed via analytic continuation to the complexified boundary, yielding representations that involve both Rindler wedges and, for interior points, complex-time contours. The results demonstrate that time-dependent bulk dynamics can be encoded in a single boundary theory, with potential generalizations to higher dimensions and more intricate collapse histories, providing a concrete framework for holography in non-static spacetimes.
Abstract
The mapping between bulk supergravity fields in anti-de Sitter space and operators in the dual boundary conformal field theory usually relies heavily on the available global symmetries. In the present work, we study a generalization of this mapping to time dependent situations, for the simple case of collapsing shock waves in two spacetime dimensions. The construction makes use of analyticity of the conformal field theory and the properties of the asymptotic bulk geometry to reconstruct the non-analytic bulk observables. Many of the features of this construction are expected to apply to higher dimensional asymptotically anti-de Sitter spacetimes and their conformal field theory duals.