# Topological Complexity in AdS3/CFT2

@article{Abt2018TopologicalCI, title={Topological Complexity in AdS3/CFT2}, author={Raimond Abt and Johanna Erdmenger and Haye Hinrichsen and Charles M. Melby-Thompson and Ren'e Meyer and Christian Northe and Ignacio A. Reyes}, journal={Fortschritte der Physik}, year={2018}, volume={66} }

We consider subregion complexity within the AdS3/CFT2 correspondence. We rewrite the volume proposal, according to which the complexity of a reduced density matrix is given by the spacetime volume contained inside the associated Ryu‐Takayanagi (RT) surface, in terms of an integral over the curvature. Using the Gauss‐Bonnet theorem we evaluate this quantity for general entangling regions and temperature. In particular, we find that the discontinuity that occurs under a change in the RT surface…

## 89 Citations

### Holographic subregion complexity from kinematic space

- MathematicsJournal of High Energy Physics
- 2019

A bstractWe consider the computation of volumes contained in a spatial slice of AdS3 in terms of observables in a dual CFT. Our main tool is kinematic space, defined either from the bulk perspective…

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A bstractWe explore the two holographic complexity proposals for the case of a 2d boundary CFT with a conformal defect. We focus on a Randall-Sundrum type model of a thin AdS2 brane embedded in AdS3.…

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- 2019

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- 2019

The main goal of this thesis is to carefully analyze aspects of the gravitational quantities conjectured to be dual to quantum complexity in the AdS/CFT correspondence. The two most promising…

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We construct renormalized holographic entanglement entropy (HEE) and subregion complexity (HSC) in the CV conjecture for asymptotically AdS$_4$ and AdS$_5$ geometries under relevant perturbations.…

### Erratum to: Geometry and complexity of path integrals in inhomogeneous CFTs

- PhysicsJournal of High Energy Physics
- 2022

Abstract
In this work we develop the path integral optimization in a class of inhomogeneous 2d CFTs constructed by putting an ordinary CFT on a space with a position dependent metric. After setting…

### Volume complexity for Janus AdS3 geometries

- PhysicsJournal of High Energy Physics
- 2021

Abstract
We investigate the complexity=volume proposal in the case of Janus AdS3 geometries, both at zero and finite temperature. The leading contribution coming from the Janus interface is a…

### Generalized Volume-Complexity For Two-Sided Hyperscaling Violating Black Branes

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In this paper, we investigate generalized volume-complexity C gen for a two-sided uncharged HV black brane in d +2 dimensions. This quantity which was recently introduced in [46], is an extension of…

### On volume subregion complexity in non-conformal theories

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- 2020

We study the volume prescription of the holographic subregion complexity in a holographic 5 dimensional model consisting of Einstein gravity coupled to a scalar field with a non-trivial potential.…

### Complexity change under conformal transformations in AdS3/CFT2

- MathematicsJournal of High Energy Physics
- 2019

A bstractUsing the volume proposal, we compute the change of complexity of holographic states caused by a small conformal transformation in AdS3/CF T2. This computation is done perturbatively to…

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