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Vijay Balasubramanian : Five Dimensions from Four: On Dimensional Transmogrification (Apr 20, 2000 4:00 PM)

Recent developments have suggested that the classical physics of gravity in a given number of dimensions can be related to a non-gravitational theory in a lower number of dimensions. I will argue that the radial direction of five-dimensional AdS space can be generated by renormalization group (RG) flow from a dual four-dimensional theory. First, I will show that integrating out the physics outside finite balls in AdS spacetime generates a family of actions that satisfies an RG-like equation. Next, I will argue that the trace of the AdS spacetime stress tensor contains analogues of field theory beta functions and gives a gravitational analogue of an RG equation. Turning things around, I will show that the conformal anomaly computed from the four-dimensional field theory dual to AdS space completely encodes the gravitational physics of the skin of the five-dimensional spacetime. Finally, I will argue that recovering the deep interior of the five-dimensional spacetime from the four-dimensional field theory will require exotic new approaches to the renormalization group.

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