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I understand the duality between the two regions of phase space (as Maldacena described it) that are Anti-de Sitter geometry and conformal field theory as an asymptotic grafting on of scale-invariant criticality (CFT) to cylinder-condition negative-cosmological-constant Einstein field equations (AdS) has been a boon to physics and string theories in particular.

I still conceptualize the AdS/CFT correspondence as a geometry. Physics has activity. It has, if you will, computation, a progression of states.

What actually happens with AdS/CFT? In terms of cause-effect? How can I go from geometry to activity?

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  • $\begingroup$ Just to put this into more familiar terms for me: by "geometry" you mean kinematics and by "activity" you mean dynamics, right? $\endgroup$ – MannyC Apr 22 at 3:08
  • $\begingroup$ I don't quite get the question... AdS space has time evolution, just like other geometries in general relativity. The duality relates scattering in AdS (particles come in from the boundary, interact, other particles exit to the boundary) to correlation functions in the CFT (each point in the CFT correlation function corresponds to an entry or exit point on the AdS boundary). Geometric excitations of the AdS space are described in terms of gravitons or black holes, which have specific duals in the CFT. $\endgroup$ – Mitchell Porter Apr 22 at 5:08

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