Abstract
In the past, the study of the divergence structure of the holographic entanglement entropy on singular boundary regions uncovered cut-off independent coefficients. These coefficients were shown to be universal and to encode important field theory data. Inspired by these lessons we study the UV divergences of subregion complexity-action (CA) in a region with corner (kink). We develop a systematic approach to study all the divergence structures, and we emphasize that the counter term that restores reparameterization invariance on the null boundaries plays a crucial role in simplifying the results and rendering them more transparent. We find that a general form of subregion CA contains a part dependent on the null generator normalizations and a part that is independent of them. The former includes a volume contribution as well as an area contribution. We comment on the origin of the area term as entanglement entropy, and point out that its presence constitutes a robust difference between the two prescriptions to calculate subregion complexity (-action vs. -volume). We also find universal log δ divergence associated with the kink feature of the subregion. Similar flat angle limit as the subregion-CV result is obtained.
Highlights
Formed, the interior grows for an exponentially large time but the holographic entanglement entropy fails to reproduce this growth [2, 3]
We develop a systematic approach to study all the divergence structures, and we emphasize that the counter term that restores reparameterization invariance on the null boundaries plays a crucial role in simplifying the results and rendering them more transparent
We comment on the origin of the area term as entanglement entropy, and point out that its presence constitutes a robust difference between the two prescriptions to calculate subregion complexity (-action vs. -volume)
Summary
Spatial subregions in the boundary theory that contain geometric singularities are known to have interesting contributions to the entanglement entropy. When the boundary has sharp features or singularities it was found in [19, 20] that there are additional contributions that are cutoff independent and universal. The c0 cone is referred to as a kink In this case the integrand in (2.4) is independent of θ and the area functional has an integration constant. In [21] the authors found that cone regions contribute to universal terms in the entanglement entropy These contributions introduce new log or log terms that are cutoff independent, Suniv(V ) =. The conical singularity introduces a set of coefficients σ(d) that encode cutoffindependent information about the CFT This same behavior for σ(d) was found for field theory calculations of entanglement in regions with sharp corners [17]. As mentioned in the Introduction, the motivation of the present work is to understand if similar cutoff independent and possibly universal contributions are present in the case of subregion complexity-action
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