Complexity-action of subregions with corners

  • Elena Caceres
  • Ming-Lei XiaoEmail author
Open Access
Regular Article - Theoretical Physics


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.


AdS-CFT Correspondence Classical Theories of Gravity Models of Quantum Gravity 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Theory Group, Department of PhysicsUniversity of TexasAustinU.S.A.
  2. 2.Institute of Theoretical PhysicsChinese Academy of SciencesBeijingPeople’s Republic of China

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