A non-perturbative construction of the de Sitter late-time boundary

TL;DR

This paper introduces a novel non-perturbative method for constructing the late-time boundary in de Sitter spacetime, involving a boundary theory with principal series operators and a new bulk-to-boundary expansion with an inversion formula.

Contribution

It develops a non-perturbative framework for de Sitter boundary construction using principal series operators and an inversion formula for bulk-to-boundary expansion.

Findings

Derived the spectral density's large dimension limit.

Established an inversion formula for bulk-to-boundary mapping.

Reproduced perturbation theory results from the boundary perspective.

Abstract

We propose a new approach for constructing the late-time conformal boundary of quantum field theory in de Sitter spacetime. A boundary theory which consists of a continuous family of primary operators residing on unitary irreducible representations, the principal series. These boundary operators exhibit two-point functions that include contact terms alongside standard CFT two-point functions. We introduce a bulk-to-boundary expansion in which a bulk operator, when pushed to the boundary, is represented as an integral over boundary operators. The kernel of this integral is related to the K\"all\'en-Lehmann spectral density, and we examine the convergence of the expansion by deriving the spectral density's large dimension limit. Additionally, we derive an inversion formula for the bulk-to-boundary expansion, where, given a bulk theory, the boundary operator content is constructed as an integral of the bulk operator times the bulk-to-boundary propagator. We verify the inversion formula by recovering the boundary two-point function and reproducing perturbation theory. Along the way, we define an operator that generates both the bulk-to-boundary and free bulk-to-bulk propagators from the boundary two-point function, proving to be a powerful tool for simplifying de Sitter diagrams.