Bulk Reconstruction in De Sitter Spacetime

TL;DR

This paper advances the bulk reconstruction program in de Sitter spacetime by resolving divergences for various fields and extending the framework to all vacua, enhancing the understanding of boundary-bulk relations.

Contribution

It provides boundary representations for scalars of all masses and higher spin fields in de Sitter space, addressing previous divergence issues and extending to all $\\alpha$-vacua.

Findings

Resolved divergence issues for higher spin fields in de Sitter bulk reconstruction.

Established boundary representations for all scalar masses and higher spin fields.

Extended the reconstruction framework from Bunch-Davies to all $\\alpha$-vacua.

Abstract

The bulk reconstruction program involves expressing local bulk fields as non-local operators on the boundary. It was initiated in the context of AdS/CFT correspondence. Attempts to extend it to de Sitter have been successful for heavy(principal series) scalar fields. For other fields, the construction ran into issues. In particular, divergences were found to appear for higher spin fields. In this paper, we resolve these issues and obtain boundary representations for scalars of all masses as well as higher spin fields. We trace the origin of the previously discovered divergences and show that the smearing function becomes distributional for certain values of mass, spin and dimension. We also extend the construction from Bunch-Davies vacuum to all $\alpha$-vacua.