Divergences in holographic complexity

By Alan P. Reynolds, S. Ross. 2016

138 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/815c365ab92cc7f910b7f7cc922c6b4af266d90d

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Citations in the corpus

Holographic complexity in Vaidya spacetimes. Part II (2018, methodology): “We note that this ambiguity was implicitly fixed in [79] by setting `ct = L.”
Comments on holographic complexity (2016, methodology): “[43] divergences in the WDW action using a additional boundary term introduced in [14], which renders the action invariant under reparameterizations of the null boundary coordinates.”
Holographic complexity in Vaidya spacetimes. Part I (2018, background): “On the other hand, it was found to modify the structure of the UV divergences in an interesting way [81] and it also modifies the details of the transient behaviour in the time evolution for an eternal black hole [46].”
Liouville action as path-integral complexity: from continuous tensor networks to AdS/CFT (2017, methodology): “On the other side, the [34] proposal, which introduces an additional boundary contribution, produces a surprising result for the d = 2 case i.”
Complexity and entanglement for thermofield double states (2018, background): “[24–50], but this research program is still in its nascent stages.”