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

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.

Figures (1)

• Figure 1: Time integration contours $\mathcal{C}_\pm$: The path integral measure in the in-in formalism is given by $\exp (i\int_{\mathcal{C}_+-\mathcal{C}_-}\!\!d\tau \int d^{d}{\boldsymbol{x}} \sqrt{-g}\,\mathcal{L})=\exp (iS_+-iS_-)$, where we defined $S_\pm=\int_{\mathcal{C}_\pm}d\tau \int d^d{\boldsymbol{x}} \sqrt{-g}\,\mathcal{L}$. In particular, $\mathcal{C}_+-\mathcal{C}_-$ forms a closed time path. We call $\mathcal{C}_+$ and $\mathcal{C}_-$ the time ordered path and the anti-time ordered path, respectively.