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arXiv · 1804.07333

Topological and Time Dependence of the Action-Complexity Relation

Musema Sinamuli·Robert B. Mann
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Abstract

We consider the dependence of the recently proposed action/complexity duality conjecture on time and on the underlying topology of the bulk spacetime. For the former, we compute the dependence of the CFT complexity on a boundary temporal parameter and find it to be commensurate with corresponding computations carried out in terms of the rate of change of the bulk action on a Wheeler deWitt (WDW) patch. For the latter, we compare the action/complexity relation for $(d+1)$-dimensional Schwarzschild AdS black holes to those of their geon counterparts, obtained via topological identification in the bulk spacetime. The complexity/action duality holds in both cases, but with the proportionality changed by a factor of 4, indicating sensitivity to spacetime topology.

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Musema Sinamuli, Robert B. Mann. 2018-04-19. Topological and Time Dependence of the Action-Complexity Relation. https://doi.org/10.1103/physrevd.98.026005

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