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arXiv · 1809.09356

Complexity-action of subregions with corners

Elena Caceres·Ming-Lei Xiao
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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 v.s. -volume). We also find universal $\log\delta$ divergence associated with the kink feature of the subregion. Similar flat angle limit as the subregion-CV result is obtained.

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Elena Caceres, Ming-Lei Xiao. 2018-09-25. Complexity-action of subregions with corners. https://doi.org/10.1007/jhep03(2019)062

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