Comments on holographic complexity

By Dean Carmi, R. Myers, Pratik Rath. Journal of High Energy Physics, 2016

309 citations recorded by the source corpus.

We study two recent conjectures for holographic complexity: the complexity=action conjecture and the complexity=volume conjecture. In particular, we examine the structure of the UV divergences appearing in these quantities, and show that the coefficients can be written as local integrals of geometric quantities in the boundary. We also consider extending these conjectures to evaluate the complexity of the mixed state produced by reducing the pure global state to a specific subregion of the boundary time slice. The UV divergences in this subregion complexity have a similar geometric structure, but there are also new divergences associated with the geometry of the surface enclosing the boundary region of interest. We discuss possible implications arising from the geometric nature of these UV divergences.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d06c56bdb67a54a064f4f6ecc00b168ffa1eaf0a

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Citations in the corpus

On the time dependence of holographic complexity (2017, methodology): “Thus, it is enough to (15)For a proposed generalization for the complexity of subsystems in terms of the co-dimension one volume enclosed by the Ryu-Takayanagi surface, see [27, 45, 46].”
Divergences in holographic complexity (2016, background): “This would produce a different set of coefficients for subleading divergences [16].”
Circuit complexity for free fermions (2018, background): “(46)With this observation, we can also see that no obvious tension between the different structure of the UV divergences found with complexity=action and complexity=volume proposals for holographic complexity [12].”
Circuit complexity in interacting QFTs and RG flows (2018, background): “Complexity equals action gives rise to a logarithmic enhancement of the volume divergence but still it doesn’t give rise to fractional volume [40].”
Liouville action as path-integral complexity: from continuous tensor networks to AdS/CFT (2017, background): “For various earlier proposals for holographic subregion complexity refer to [23, 26].”
Circuit complexity in quantum field theory (2017, background): “Our experience with holographic complexity suggests that we will not be able to sensibly define complexity in a QFT without a UV regulator in place [19].”
Complexity and entanglement for thermofield double states (2018, methodology): “xity proposals. First, the complexity of the vacuum state diverges as the spatial volume occupied by a boundary quantum eld theory measured in the units of the UV cut-o with a non-universal prefactor [29]. Furthermore, for the CA proposal, there is a possibility that this leading divergence is also ”
Circuit complexity for coherent states (2018, background): “1) found for holographic complexity [21] and hence the κ measures (1.”
Holographic complexity in Vaidya spacetimes. Part II (2018, methodology): “To remove the AdS scale from C̃UV A , [26] suggested that one should choose”
Holographic complexity in Vaidya spacetimes. Part I (2018, methodology): “Similarly, there should be an overall flip of the sign of this surface term in appendix A of [35], i.”