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

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.