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Divergences in Holographic Complexity

Reynolds, Alan; Ross, Simon F.

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Alan Reynolds


We study the UV divergences in the action of the 'Wheeler-de Witt patch' in asymptotically AdS spacetimes, which has been conjectured to be dual to the computational complexity of the state of the dual field theory on a spatial slice of the boundary. We show that including a surface term in the action on the null boundaries which ensures invariance under coordinate transformations has the additional virtue of removing a stronger than expected divergence, making the leading divergence proportional to the proper volume of the boundary spatial slice. We compare the divergences in the action to divergences in the volume of a maximal spatial slice in the bulk, finding that the qualitative structure is the same, but subleading divergences have different relative coefficients in the two cases.


Reynolds, A., & Ross, S. F. (2017). Divergences in Holographic Complexity. Classical and Quantum Gravity, 34(10), Article 105004.

Journal Article Type Article
Acceptance Date Mar 24, 2017
Online Publication Date Apr 13, 2017
Publication Date May 18, 2017
Deposit Date Mar 28, 2017
Publicly Available Date Apr 13, 2018
Journal Classical and Quantum Gravity
Print ISSN 0264-9381
Electronic ISSN 1361-6382
Publisher IOP Publishing
Peer Reviewed Peer Reviewed
Volume 34
Issue 10
Article Number 105004
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