Anti-de Sitter space is a solution to Einstein’s field equations that is negatively curved everywhere. It is analogous to the geometry of Eschers’s “Angels and devils", in which you have to imagine that all the angels and devils are the same size but that they are distorted due to the negative curvature of space (in the same way that Mercator’s projection of the globe misrepresents the area of continents away from the equator). This figure depicts anti-de Sitter space at an instant; the vertical dimension is time. The geometry is bounded by the surface of the cylinder and the holographic principle states that quantum gravity in the interior of the space is described by a quantum field theory, such as QCD, on the boundary.
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