Figure 1 (IMAGE)

Kavli Institute for the Physics and Mathematics of the Universe

Figure 1

Caption

A diagram used to prove that quantum gravity cannot have any global symmetry. Symmetry, if existed, could act only on the shaded regions in the diagram and causes no change around the black spot in the middle. The shaded regions can be made as small as we like by dividing the boundary circle more and more. Thus, the alleged symmetry would not act anywhere inside of the circle. Contradiction.

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Harlow and Ooguri

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