On the role of counterterms in holographic complexity
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DOI10.1007/JHEP11(2019)054zbMATH Open1429.83075arXiv1906.09561WikidataQ126777711 ScholiaQ126777711MaRDI QIDQ2292474
Author name not available (Why is that?)
Publication date: 3 February 2020
Published in: (Search for Journal in Brave)
Abstract: We consider the Complexity=Action (CA) proposal in Einstein gravity and investigate new counterterms which are able to remove all the UV divergences of holographic complexity. We first show that the two different methods for regularizing the gravitational on-shell action proposed in Ref. cite{Carmi:2016wjl} are completely equivalent, provided that one considers the Gibbons-Hawking-York term as well as new counterterms inspired from holographic renormalization on timelike boundaries of the WDW patch. Next, we introduce new counterterms on the null boundaries of the WDW patch for four and five dimensional asymptotically AdS spacetimes which are able to remove all the UV divergences of the on-shell action. Moreover, they are covariant and do not change the equations of motion. At the end, by applying the null counterterms, we calculate the holographic complexity of an AdS-Schwarzschild black hole as well as the complexity of formation. We show that the null counterterms do not change the complexity of formation.
Full work available at URL: https://arxiv.org/abs/1906.09561
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