Aspects of dS/CFT holography

A bstract It has been suggested that a dS d +1 spacetime of radius R ds has a holographic dual, living at future space-like infinity $$ \mathcal{I} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>I</mml:mi> </mml:math> + , with the bulk wave function being dual to the partition function of the boundary theory, [1]. We consider some aspects of this correspondence. For under damped scalars with mass $$ {M}^2{R}_{ds}^2&gt;\frac{d^2}{4} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>M</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:msubsup> <mml:mi>R</mml:mi> <mml:mi>ds</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo>&gt;</mml:mo> <mml:mfrac> <mml:msup> <mml:mi>d</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mn>4</mml:mn> </mml:mfrac> </mml:math> , belonging to the principal series, we show that for the Bunch Davies vacuum a suitable source in the boundary theory can be identified in terms of the coherent state representation of the wave function. We argue that terms in the resulting correlation functions, which are independent of the late time cut-off, satisfy the Ward identities of a conformal field theory. We also discuss other ways to identify sources, both in the under damped and the over damped case, where $$ {M}^2{R}_{ds}^2&lt;\frac{d^2}{4} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>M</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:msubsup> <mml:mi>R</mml:mi> <mml:mi>ds</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo>&lt;</mml:mo> <mml:mfrac> <mml:msup> <mml:mi>d</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mn>4</mml:mn> </mml:mfrac> </mml:math> , and argue that these too can lead to correlators satisfying the Ward identities of a CFT. Some comments on the violation of reflection positivity, and the cut-off dependent terms, along with some explicit checks and sample calculations, are also included.