>>11294180The core idea, of which the AdS/CFT correspondence was the first concrete realization, is that descriptions/models of certain d-dimensional physical systems that do not include gravity can be equivalently described by a model of higher-dimensional gravity, hence the more general name "gauge/gravity duality". Equivalent here means that both descriptions agree precisely on all predictions for the behaviour of the system.
>>11296173The above incorporates the holographic principle because it describes a correspondence between a higher and a lower-dimensional system. This was originally considered in the context of black-hole physics, inspired by the fact that the entropy of a black hole is proportional to its area (2d), not its volume (3d). The term holographic is used because it is analogous to a hologram: a 3d image is encoded in a 2d surface.
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