Abstract
We refine the calculation of holographic complexity of black holes in the complexity equals action approach by applying the recently introduced criterion that the action of any causal diamond in static vacuum regions must vanish identically. This criterion fixes empty anti--de Sitter (AdS) spacetime as the reference state with vanishing complexity and renders holographic complexity explicitly finite in all the cases we consider. The cases considered here include the Reissner-Nordstr\"om-AdS black hole, the rotating BTZ black hole, the Kerr-AdS black hole, and AdS-Vaidya spacetime. The criterion is equivalent to imposing that the corner contributions vanish. Contrary to earlier results, we find that the generalized Lloyd bound always holds in the Reissner-Nordstr\"om-AdS and BTZ cases.
Highlights
The application of concepts and ideas of information theory to quantum field theory and gravity has been proven to be a fruitful line of research, especially in the context of the anti–de Sitter (AdS)=CFT correspondence [1,2,3,4,5,6]
Computational complexity is a measure of how difficult it is to approximately compute a desired target state starting from a given reference state and using a certain set of elementary operations [7]
The definition of computational, or circuit, complexity depends on the system under consideration, the set of elementary operations, the reference state and a parameter ε that specifies the tolerance with which the target state is reached
Summary
The application of concepts and ideas of information theory to quantum field theory and gravity has been proven to be a fruitful line of research, especially in the context of the AdS=CFT correspondence [1,2,3,4,5,6]. Given the variety of complexity measures that one can define in quantum and information theory, it is no surprise that several gravitational observables in asymptotically anti–de Sitter (AdS) spacetime have been proposed as holographic duals of complexity. In a recent paper [21], we have proposed a refinement of the C 1⁄4 A approach introducing the criterion that the action in any causal diamond in static vacuum regions should vanish With this criterion, the complexity of the state dual to pure AdS spacetime vanishes by construction, which identifies this state as the reference state. The approach taken in [21] aims to identify a privileged choice of parametrization by imposing the criterion of vanishing action on any static vacuum causal diamond This criterion defines the state dual to empty AdS space as the reference state, because it has zero complexity by construction.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
