Divergences in Holographic Complexity

Reynolds, Alan; Ross, Simon F.

Abstract

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.

Citation

Reynolds, A., & Ross, S. F. (2017). Divergences in Holographic Complexity. Classical and Quantum Gravity, 34(10), Article 105004. https://doi.org/10.1088/1361-6382/aa6925

• 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
• DOI: https://doi.org/10.1088/1361-6382/aa6925
• Public URL: https://durham-repository.worktribe.com/output/1360528
• Related Public URLs: https://arxiv.org/abs/1612.05439