# The dS/CFT correspondence Like anti-de Sitter space, (Lorentzian) de Sitter space has a boundary. One is therefore tempted to study the correspondence between de Sitter quantum gravity and a theory of dual CFT. Unlike in AdS/CFT, the boundaries of de Sitter live at the future and the past, and are spacelike. This is an important difference between AdS/CFT and dS/CFT. ## Unitarity In AdS/CFT, unitarity of the bulk theory carries to the boundary, because the boundary is timelike. The argument fails in dS/CFT, so the dual CFT is generally non-unitary. ## Wavefunction vs partition function It is often said that the partition function of the CFT is dual to the wavefunction of the universe in dS/CFT, rather than the partition function of the bulk gravity theory. This is another stark contrast to AdS/CFT. ## Refs - [[2001#Strominger]] - [[Witten2001]] - [[Maldacena2002]] - general thoughts by Susskind: [talk](https://www.youtube.com/watch?v=4GKjr-y5MY0&ab_channel=InstituteforAdvancedStudy) ## Basic questions - [[2026#Nakayama]]: the CFT dual to de Sitter is not unitary, but unitarity is needed in establishing that scale-invariance implies conformal invariance; this paper uses a toy modified theory of gravity to demonstrate this issue in dS/CFT ## Realisations - [[0421 Higher-spin gravity|higher spin gravity]]: [[AnninosHartmanStrominger2011]][](http://arxiv.org/abs/1108.5735) - Einstein gravity: [[HikidaNishiokaTakayanagiTaki2021]][](http://arxiv.org/abs/2110.03197) and [[HikidaNishiokaTakayanagiTaki2022]][](http://arxiv.org/abs/2203.02852) - 2d dS - [[MaldacenaTuriaciYang2019]][](http://arxiv.org/abs/1904.01911) - [[CotlerJensenMaloney2019]][](http://arxiv.org/abs/1905.03780) ## dS/CFT v.s. FRW/CFT - the relation is non-trivial - [[HarlowSusskind2010]] ## RT for dS - [[2021#Shaghoulian]] - [[ShaghoulianSusskind2022]][](https://arxiv.org/abs/2201.03603)