Surface counterterms and regularized holographic complexity

@article{Yang2017SurfaceCA,
  title={Surface counterterms and regularized holographic complexity},
  author={Run-Qiu Yang and Chao Niu and Keun-Young Kim},
  journal={Journal of High Energy Physics},
  year={2017},
  volume={2017},
  pages={1-42}
}
A bstractThe holographic complexity is UV divergent. As a finite complexity, we propose a “regularized complexity” by employing a similar method to the holographic renor-malization. We add codimension-two boundary counterterms which do not contain any boundary stress tensor information. It means that we subtract only non-dynamic back-ground and all the dynamic information of holographic complexity is contained in the regularized part. After showing the general counterterms for both CA and CV… 
View on Springer
[PDF] Semantic Reader
70 Citations
Highly Influential Citations
1
Background Citations
19
Methods Citations
6
Results Citations
5

70 Citations

Renormalized holographic subregion complexity under relevant perturbations

We construct renormalized holographic entanglement entropy (HEE) and subregion complexity (HSC) in the CV conjecture for asymptotically AdS4 and AdS5 geometries under relevant perturbations. Using…

On the role of counterterms in holographic complexity

We consider the Complexity=Action (CA) proposal in Einstein gravity and investigate new counterterms which are able to remove all the UV divergences of holographic complexity. We first show that the…

Reparameterization dependence is useful for holographic complexity

Holographic complexity in the “complexity equals action” approach is reconsidered relaxing the requirement of reparameterization invariance of the action with the prescription that the action vanish…

Holographic complexity of anisotropic black branes

We use the complexity = action (CA) conjecture to study the full-time dependence of holographic complexity in anisotropic black branes. We find that the time behaviour of holographic complexity of…

Complexity of holographic superconductors

A bstractWe study the complexity of holographic superconductors (Einstein-Maxwell-complex scalar actions in d + 1 dimension) by the “complexity = volume” (CV) conjecture. First, it seems that there…

Switchback effect of holographic complexity in multiple-horizon black holes

In this paper, we use the “complexity equals action” (CA) conjecture to explore the switchback effect in the strongly-coupled quantum field theories with finite N and finite coupling effects. In the…

Switchback effect of holographic complexity in multiple-horizon black holes

In this paper, we use the “complexity equals action” (CA) conjecture to explore the switchback effect in the strongly-coupled quantum field theories with finite N and finite coupling effects. In the…

Subsystem complexity in warped AdS

We compute the ultraviolet divergences of holographic subregion complexity for the left and right factors of the thermofield double state in warped AdS3 black holes, both for the action and the…

Complexity in de Sitter space

We consider the holographic complexity conjectures for de-Sitter invariant states in a quantum field theory on de Sitter space, dual to asymptotically anti-de Sitter geometries with de Sitter…

On complexity of holographic flavors

A bstractQuantum complexity of a thermofield double state in a strongly coupled quantum field theory has been argued to be holographically related to the action evaluated on the Wheeler-DeWitt patch.…
...

References

SHOWING 1-10 OF 43 REFERENCES

Complexity of formation in holography

A bstractIt was recently conjectured that the quantum complexity of a holographic boundary state can be computed by evaluating the gravitational action on a bulk region known as the Wheeler-DeWitt…

Holographic Complexity

For a field theory with a gravitational dual, following Susskind’s proposal we define holographic complexity for a subsystem. The holographic complexity is proportional to the volume of a codimension…

Holographic Complexity Equals Bulk Action?

The hypothesis that black holes are the fastest computers in nature is discussed and the conjecture that the quantum complexity of a holographic state is dual to the action of a certain spacetime region that is called a Wheeler-DeWitt patch is illustrated.

Divergences in holographic complexity

We study the UV divergences in the action of the ‘Wheeler-de Witt patch’ in asymptotically AdS spacetimes, which has been conjectured to be dual to the computational complexity of the state of the…

Some calculable contributions to holographic entanglement entropy

Using the AdS/CFT correspondence, entanglement entropy for a boundary theory deformed by a relevant operator is examined and it is shown that the relevant deformation introduces new logarithmic contributions to the entangled entropy.

Surface terms as counterterms in the AdS-CFT correspondence

We examine the recently proposed technique of adding boundary counterterms to the gravitational action for spacetimes which are locally asymptotic to anti\char21{}de Sitter spacetimes. In particular,…

Aspects of Holographic Entanglement Entropy

This is an extended version of our short report [1], where a holographic interpretation of entanglement entropy in conformal field theories is proposed from AdS/CFT correspondence. In addition to a…

Holographic entanglement entropy close to quantum phase transitions

A bstractWe investigate the holographic entanglement entropy (HEE) of a strip geometry in four dimensional Q-lattice backgrounds, which exhibit metal-insulator transitions in the dual field theory.…

Lecture notes on holographic renormalization

We review the formalism of holographic renormalization. We start by discussing mathematical results on asymptotically anti-de Sitter (AdS) spacetimes. We then outline the general method of…

Holographic Renormalization