Complexity of formation in holography

By Shira Chapman, H. Marrochio, R. Myers. 2016

253 citations recorded by the source corpus.

A bstractIt was recently conjectured that the quantum complexity of a holographic boundary state can be computed by evaluating the gravitational action on a bulk region known as the Wheeler-DeWitt patch. We apply this complexity=action duality to evaluate the ‘complexity of formation’ [1, 2], i.e. the additional complexity arising in preparing the entangled thermofield double state with two copies of the boundary CFT compared to preparing the individual vacuum states of the two copies. We find that for boundary dimensions d > 2, the difference in the complexities grows linearly with the thermal entropy at high temperatures. For the special case d = 2, the complexity of formation is a fixed constant, independent of the temperature. We compare these results to those found using the complexity=volume duality.

Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/2f51335346f14b8af3f41f864a7f57348ddae856

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Citations in the corpus

Comments on holographic complexity (2016, background): “However, these contributions were examined in detail in [38] and were shown to vanish there.”
Liouville action as path-integral complexity: from continuous tensor networks to AdS/CFT (2017, background): “In a related direction a quantity called complexity of formation was defined and studied in [33].”
Complexity and entanglement for thermofield double states (2018, methodology): “ a (d 2)-sphere, i.e., d 2 = 2ˇ d 1 = d 1 2 . The complexity of formation for holographic CFTs in a at decompactied space is directly proportional to the entropy, for d3 in both CA and CV proposals [27]. Therefore, it is natural to normalize the complexity of formation by the entropy. Let us then co”
Quantum extremal islands made easy. Part II. Black holes on the brane (2020, methodology): “of the area functional with the following convenient gauge choice p 2(r d1)_v2 + 2_vr_ = r 2 : (3.32) 13We extend our dention of r tor ( ) across the horizon using the standard prescription given in [92]. { 25 { The integrand in eq. (3.31) is independent of vand so we have a conserved ‘vmomentum’ P ”
Divergences in holographic complexity (2016, background): “1 Another way to cancel UV contributions is to consider the difference between two spacetimes with the same asymptotic structure, as in [11].”
On the time dependence of holographic complexity (2017, methodology): “Using the CV conjecture, the late time growth rate of the complexity also saturates, but this final rate is only proportional to the mass at high temperatures and with a coefficient that depends on the spacetime dimension [6, 26].”
Chaos and complexity by design (2016, background): “stion of whether Bob can reconstruct Alice’s secret is related to the decay of an average of a certain set of OTO four-point correlators. 26This is also a question of interest in holography, see e.g. [66]. 27We thank Patrick Hayden and Michael Walter for initial discussions about this idea. 41 In xF”
Holographic complexity in Vaidya spacetimes. Part I (2018, methodology): “If we fix the profile fp(v) = ω d−2 to be a fixed constant, these metrics would correspond precisely to the black hole geometries in d ≥ 3 for which the holographic complexity was studied in [34, 46].”
Holographic complexity in Vaidya spacetimes. Part II (2018, methodology): “The latter was evaluated in [22], where we found ∆CNS = −c/3 when subtracting the complexity of the Neveu-Schwarz vacuum (i.”