Double Trace Flows and Holographic RG in dS/CFT correspondence

TL;DR

This paper explores how holographic RG flows in de Sitter space influence dual non-unitary field theories, revealing real correlation functions and beta functions under certain conditions, and highlighting differences from AdS/CFT correspondence.

Contribution

It demonstrates the form of beta functions for double trace couplings in dS/CFT and analyzes conditions for real correlation functions and RG flows, especially in dS(4) and even-dimensional cases.

Findings

Real n-point functions possible in dS(4) with proper normalization.

IR fixed point at negative coupling in certain dS models.

No normalization ensures real beta coefficients in even-dimensional dS.

Abstract

If there is a dS/CFT correspondence, time evolution in the bulk should translate to RG flows in the dual euclidean field theory. Consequently, although the dual field is expected to be non-unitary, its RG flows will carry an imprint of the unitary time evolution in the bulk. In this note we examine the prediction of holographic RG in de Sitter space for the flow of double and triple trace couplings in any proposed dual. We show quite generally that the correct form of the field theory beta functions for the double trace couplings is obtained from holography, provided one identifies the scale of the field theory with (i|T|) where T is the `time' in conformal coordinates. For dS(4), we find that with an appropriate choice of operator normalization, it is possible to have real n-point correlation functions as well as beta functions with real coefficients. This choice leads to an RG flow with an IR fixed point at negative coupling unlike in a unitary theory where the IR fixed point is at positive coupling. The proposed correspondence of Sp(N) vector models with de Sitter Vasiliev gravity provides a specific example of such a phenomenon. For dS(d+1) with even d, however, we find that no choice of operator normalization exists which ensures reality of coefficients of the beta-functions as well as absence of n-dependent phases for various n-point functions, as long as one assumes real coupling constants in the bulk Lagrangian.