Why Is AdS Space Ideal for Formulating String Theory and Holography?

[dx]

In AdS/CFT, we have the GKP-witten relation

$$\left< \exp \left( i \int \phi^{(0)} O \right) \right> = e^{-S[\phi^{(0)}]}$$

why is it natural to formulate string theory on an AdS space? is it a natural background for some particular definite reasons? Is holography naturally formulated in an AdS background?

 

[AndyW]

The AdS/CFT correspondence is a powerful tool that allows us to connect two seemingly different theories: AdS (Anti-de Sitter) space, which is a curved spacetime in string theory, and CFT (conformal field theory), which is a quantum field theory without gravity. This relation was first proposed by Juan Maldacena in 1997 and has since been extensively studied and verified by many researchers.

One of the main reasons why it is natural to formulate string theory on an AdS space is because AdS space is a maximally symmetric space, meaning that it has a high degree of symmetry. This makes it a very useful and versatile background for studying string theory, as it allows for simpler calculations and a better understanding of the theory.

Additionally, AdS space has some unique properties that make it an ideal background for studying holography. AdS space has a boundary at infinity, and the behavior of fields near this boundary is closely related to the behavior of fields in the bulk of the space. This is a key aspect of the AdS/CFT correspondence, where the CFT on the boundary is equivalent to the string theory in the bulk.

Furthermore, AdS space has a negative cosmological constant, which is crucial for the holographic principle to hold. This principle states that the information of a higher-dimensional space can be encoded on the boundary of a lower-dimensional space. In the case of AdS space, this means that the information in the bulk can be encoded on the boundary, allowing us to study the theory in a lower-dimensional space.

In summary, the AdS/CFT correspondence is a natural and powerful tool for studying string theory and holography, and AdS space provides a suitable background for this correspondence due to its high degree of symmetry, boundary behavior, and negative cosmological constant.