Wavefunctions in dS/CFT revisited: principal series and double-trace deformations

TL;DR

This paper investigates wavefunctions of heavy scalars in de Sitter space, revealing their interpretation as two-point functions on a cyclic RG flow due to double-trace deformations in the dual CFT, thus refining the dS/CFT correspondence.

Contribution

It demonstrates that heavy scalar wavefunctions in dS can be understood via double-trace deformations, providing a new dictionary relating de Sitter and conformal two-point functions.

Findings

Heavy scalars oscillate outside the horizon unlike light fields.

Quadratic wavefunction terms relate to cyclic RG flows.

New dS/CFT dictionary for two-point functions.

Abstract

We study wavefunctions of heavy scalars on de Sitter spacetime and their implications to dS/CFT correspondence. In contrast to light fields in the complementary series, heavy fields in the principal series oscillate outside the cosmological horizon. As a consequence, the quadratic term in the wavefunction does not follow a simple scaling and so it is hard to identify it with a conformal two-point function. In this paper, we demonstrate that it should be interpreted as a two-point function on a cyclic RG flow which is obtained by double-trace deformations of the dual CFT. This is analogous to the situation in nonrelativistic AdS/CFT with a bulk scalar whose mass squared is below the Breitenlohner-Freedman (BF) bound. We also provide a new dS/CFT dictionary relating de Sitter two-point functions and conformal two-point functions in the would-be dual CFT.