Remark About dS/CFT Correspondence

TL;DR

This paper explores the dS/CFT correspondence, focusing on how Witten's non-standard inner product relates to CFT correlators, proposing a link between de Sitter space states and Euclidean CFT states.

Contribution

It introduces a conjecture connecting Witten's inner product with the Hilbert space of Euclidean CFT, providing a new perspective on de Sitter holography.

Findings

Witten's inner product relates to CFT correlators in de Sitter space.

The Hilbert space of initial states in de Sitter corresponds to Euclidean CFT states.

CFT correlators can be derived in various vacuum states from this framework.

Abstract

In this paper we will study some aspects of dS/CFT correspondence. We will focus on the relation between Witten's non-standard de Sitter inner product and correlators in the holographic dual conformal field theory. We will argue that from the definition of Witten's inner product and conjecture that the Hilbert space of initial states of massive scalar field on $\mathcal{I}^-$ in de Sitter space corresponds to the Hilbert space of states of Euclidean CFT on $\mathcal{I}^-$, we can obtain CFT correlators in any vacuum state.