Universal pieces of holographic entanglement entropy and holographic subregion complexity

We propose that the definition of holographic subregion complexity 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 ${\mathrm{AdS}}_6$ solutions of type IIA supergravity. This modified definition ensures that the universal piece of the holographic subregion complexity 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 behavior 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 the field theoretical analogue of holographic subregion complexity and the sphere partition function or Weyl $a$-anomaly in odd or even dimensions, respectively.