Holographic Complexity from the Crofton's Formula in Lorentzian AdS${}_3$

Abstract

We study the Crofton's formula in the Lorentzian AdS${}_3$ 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.

arXiv comment23 pages,5 figures,v2: references added

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Cited by in corpus (2)

• Weaving the (AdS) spaces with partial entanglement entropy threads
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