AdS3CFT2

Anti-de Sitter space in three dimensions, denoted AdS3, is a spacetime with constant negative Ricci curvature. When we consider a quantum field theory living on the boundary of this space, we often find a two-dimensional conformal field theory, or CFT2. The correspondence between these two is known as the AdS3/CFT2 correspondence. This is a specific instance of the broader AdS/CFT correspondence, which postulates a duality between a theory of gravity in an Anti-de Sitter spacetime and a quantum field theory on its boundary.

The AdS3/CFT2 duality has been a fertile ground for studying quantum gravity and strongly coupled quantum field theories. In this specific case, the boundary CFT2 often exhibits remarkable properties. For instance, it can be a theory of free bosons or fermions, or it can be a more complex interacting theory. The dual gravitational description in AdS3 can involve string theory or supergravity. One of the key insights comes from the work of Strominger and Witten, which relates certain topological quantum field theories in three dimensions to chiral conformal field theories in two dimensions.

The correspondence allows physicists to translate problems that are difficult to solve in one domain into simpler problems in the other. For example, calculating correlation functions in a strongly coupled CFT2 might be mapped to computing geodesic lengths in the bulk AdS3 spacetime. Conversely, understanding the spectrum of states in a quantum gravity theory in AdS3 can shed light on the properties of its dual CFT2. This duality is particularly relevant in the study of black holes, where the holographic principle suggests that the degrees of freedom of a gravitational system can be described by a lower-dimensional quantum field theory.