$AdS/CFT$ to $dS/CFT$: Some Recent Developments

TL;DR

This paper provides a pedagogical overview of the AdS/CFT correspondence and explores recent developments extending holography concepts to de Sitter and flat spacetimes, highlighting foundational ideas and consistency checks.

Contribution

It offers a comprehensive introduction to holography, detailing the extension of AdS/CFT to de Sitter and flat spacetimes, which is a recent advancement in the field.

Findings

Review of conformal field theory and AdS spacetime fundamentals

Discussion of consistency checks supporting AdS/CFT

Brief exploration of holography in de Sitter and flat spacetimes

Abstract

These lecture notes aim to provide a pedagogical introduction to the AdS/CFT correspondence and its extensions to spacetimes with positive (de Sitter spacetime) and zero (flat spacetime) cosmological constant. We begin by explaining the physical motivation for holography and the significance of the AdS/CFT correspondence. We then review the basic ingredients of conformal field theory (CFT) and anti de Sitter (AdS) spacetime required to formulate the duality. Building on these foundations, we discuss the formulation of the AdS/CFT correspondence and discuss several consistency checks that support it. We conclude with a brief discussion of holography in de Sitter and flat spacetimes.