Topological and Time Dependence of the Action-Complexity Relation

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.

12 pages, 4 figures

References in corpus (6)

• Gravitational action with null boundaries
• On the Time Dependence of Holographic Complexity
• Holographic complexity is nonlocal
• Evolution of Complexity Following a Global Quench
• Divergences in the rate of complexification
• Behind the geon horizon

Cited by in corpus (6)

• Complexity and entanglement for thermofield double states
• Time Dependence of Holographic Complexity in Gauss-Bonnet Gravity
• Entanglement Harvesting with a Twist
• Holographic Subregion Complexity in Einstein-Born-Infeld theory
• Holographic Complexity and Charged Scalar Fields
• Holographic complexity of rotating black holes