Universal Pieces of Holographic Entanglement Entropy and Holographic Subregion Complexity

Abstract

We propose that the definition of holographic subregion complexity (HSC) needs a slight modification for supergravity solutions with warped anti-de Sitter (AdS) factors. Such warp factors can arise due to the nontrivial dilaton profile, for example, in $Ad{S}_6$ solutions of type IIA supergravity. This modified definition ensures that the universal piece of the HSC is proportional to that of the holographic entanglement entropy, as is the case for supergravity solutions without warp factors. This also means that the leading behaviour at large $N$ is the same for both these quantities, as we show for some well-known supergravity solutions (with and without warp factors) in various dimensions. We also show that this relation between the universal pieces suggests "universal" relations between field theoretical analogue of HSC and the sphere partition function or Weyl $a$-anomaly in odd or even dimensions, respectively.

v1: 18 pages; v2 & v3: 19 pages, title changed, sections 1 and 2 updated, references added, journal-ref added; v4: typos corrected, minor changes to text (published version)

References in corpus (14)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Towards a derivation of holographic entanglement entropy
• Complexity and Shock Wave Geometries
• Holographic c-theorems in arbitrary dimensions
• Quantum Computation as Geometry
• Entanglement as a Probe of Confinement
• Liouville Action as Path-Integral Complexity: From Continuous Tensor Networks to AdS/CFT
• On non-abelian T-dual geometries with Ramond fluxes
• On Volumes of Subregions in Holography and Complexity
• Type IIB Supergravity Solutions with AdS${}_5$ From Abelian and Non-Abelian T Dualities
• Universal RG Flows Across Dimensions and Holography
• Holographic Aspects of Four Dimensional $\mathcal{N}=2$ SCFTs and their Marginal Deformations
• Integrability and Holographic Aspects of Six-Dimensional $\mathcal{N}=(1,0)$ Superconformal Field Theories
• Entanglement entropy and complexity of singular subregions in deformed CFT

Cited by in corpus (4)

• Holographic study of entanglement and complexity for mixed states
• Entanglement wedge cross section for noncommutative Yang-Mills theory
• Gauss-Bonnet AdS planar and spherical black hole thermodynamics and holography
• Klein-Gordon and Schrödinger solutions in Lovelock quantum gravity