Holographic Complexity from the Crofton's Formula in Lorentzian AdS3
Abstract
We study the Crofton's formula in the Lorentzian AdS3 and find that the area of a generic space-like two dimensional surface is given by the flux of space-like geodesics. The "complexity=volume" conjecture then implies a new holographic representation of the complexity in terms of the number of geodesics. Finally, we explore the possible explanation of this result from the standpoint of information theory.
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