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Divergences in holographic complexity.

Reynolds, Alan and Ross, Simon F. (2017) 'Divergences in holographic complexity.', Classical and quantum gravity., 34 (10). p. 105004.


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.

Item Type:Article
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
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Publisher statement:This is an author-created, un-copyedited version of an article published in Classical and Quantum Gravity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at
Date accepted:24 March 2017
Date deposited:03 April 2017
Date of first online publication:13 April 2017
Date first made open access:13 April 2018

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