Universal Pieces of Holographic Entanglement Entropy and Holographic Subregion Complexity

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.