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

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AdS space is considered ideal for formulating string theory and holography due to its unique geometric properties that facilitate the application of the AdS/CFT correspondence. The GKP-Witten relation illustrates the connection between quantum field theories and gravity in higher dimensions, making AdS a natural setting for these theories. The curvature of AdS space allows for a well-defined boundary, which is essential for holographic principles. Additionally, the presence of conformal symmetry in AdS spaces supports the formulation of holographic dualities. Overall, the characteristics of AdS space provide a robust framework for exploring the interplay between quantum gravity and field theories.
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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?
 

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