I will speak about my recent research on mechanism of AdS geometry emerging from conformal field theory (CFT) using flow equations.
A flow equation is conceptually equivalent to a block spin transformation, which describes course-graining of observables.
A characteristic of flow equations is that operators are non-locally transformed in such a way that their contact singularity is resolved, which is crucial for the construction of a bulk holographic space. I will explain our main results given as follows.
i) The induced metric associated with the flow equation becomes identical to the quantum information metric.
ii) The induced metric for any CFT defined on flat space matches the Poincare AdS one.
iii) The conformal transformations of CFT converts to the isometries of AdS space after taking vacuum expected value.
iv) We extended ii) and iii) to the case of CFT defined on a general conformally flat manifold. In particular we constructed a metric of AdS space whose boundary is given by the curved manifold.
v) By using this formulation we proposed how to compute the quantum correction to a bulk observable. In particular we computed the quantum correction of the bulk cosmological constant of a free higher spin theory on the AdS space.