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.

From locality and unitarity to cosmological correlators

“…Much information has emerged from improvements in perturbative calculations [1][2][3][4][5][6][7][8][9][10][11][12]. At the same time, it has become clear that very powerful results can be bootstrapped directly from fundamental principles taking advantage of the restrictive symmetries of de Sitter spacetime [13][14][15][16][17][18][19][20][21][22][23][24][25][26]. For these bootstrap methods to make contact with the rich world of inflationary phenomenology and eventually observations, it is necessary to abandon the requirement of full de Sitter isometries since de Sitter boosts are incompatible with large primordial non-Gaussianities [27].…”

Dispersion formulas in QFTs, CFTs and holography

“…First, we will prove (5.44), which gives the large t scaling of g t ∆,J as a function of ∆ φ . From this result, we can prove (5.47)-(5.49), which gives the effective spins, J 0 andJ 0 , of the Polyakov-Regge block P t|s ∆,J as a function of ∆ φ 42 Alternatively, one can use that K φ (p) comes from a bulk time-ordered correlator in free-field theory.…”

“…Similar questions have also been studied in the cosmological bootstrap [32][33][34][35][36][37][38][39], where inflationary correlators are fixed using consistency conditions such as factorization, the absence of folded singularities, and conformal symmetry. To relate on-shell methods in AdS/CFT and dS, we recall that in perturbation theory the AdS partition function is related by analytic continuation to the dS wavefunction [40][41][42]. Based on insights from the modern amplitudes program [43], it is natural to expect that on-shell methods for AdS and dS correlators will reveal new symmetries and structures that are not manifest using a Lagrangian approach.…”

Unitarity at the late time boundary of de Sitter

“…A general approach in using the wavefunction method on de Sitter is to compute the Euclidean Anti de Sitter (EAdS) partition function and analytically continue the result to de Sitter. While the present work was being completed, there appeared the work of [34] who also consider the de Sitter wavefunction for scalar fields. Similar to this work we carry all our calculations on de Sitter, in Poincaré coordinates where the metric takes the form…”

“…Our section 2.1 can be considered as a short review of some of their results. In complementary series two-point functions one can neglect the contribution of the operator with the higher scaling dimension, β N , and the authors of [34] do make this simplification. However, we are interested to track how both operators enter the twopoint functions precisely and for this purpose we do not eliminate the contribution of the operator with the higher scaling dimension in the complementary series case.…”