2023
DOI: 10.1007/jhep01(2023)154
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Complexity equals anything II

Abstract: We expand on our results in [1] to present a broad new class of gravitational observables in asymptotically Anti-de Sitter space living on general codimension-zero regions of the bulk spacetime. By taking distinct limits, these observables can reduce to well-studied holographic complexity proposals, e.g., the volume of the maximal slice and the action or spacetime volume of the Wheeler-DeWitt patch. As with the codimension-one family found in [1], these new observables display two key universal features for th… Show more

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Cited by 42 publications
(51 citation statements)
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“…However, this understanding is missing for CA. Furthermore, recently, it was shown [19,20] that CV and CA are just two members of an infinite family of observables that exhibit the linear growth and switchback behavior of complexity. This freedom in the definition of holographic complexity need not be perceived as a drawback; rather, it can be seen as a holographic feature that reflects the ambiguities existing in the definition of quantum complexity.…”
Section: Jhep04(2024)010mentioning
confidence: 99%
See 2 more Smart Citations
“…However, this understanding is missing for CA. Furthermore, recently, it was shown [19,20] that CV and CA are just two members of an infinite family of observables that exhibit the linear growth and switchback behavior of complexity. This freedom in the definition of holographic complexity need not be perceived as a drawback; rather, it can be seen as a holographic feature that reflects the ambiguities existing in the definition of quantum complexity.…”
Section: Jhep04(2024)010mentioning
confidence: 99%
“…The generalized volume complexities [19] are codimension-one, i.e. d−dimensional, observables 2 that involve 1 We use the term "generalized complexities" to refer to the observables obtained from the "complexity = anything" proposal of [19,20]. We adopt this name to emphasize that these observables are a generalization of the CV, CA, and CV2.0 proposals.…”
Section: Jhep04(2024)010mentioning
confidence: 99%
See 1 more Smart Citation
“…This growth is linear with the slope given by Lloyd's bound [16], which is twice of the energy of the state. The linear growth of quantum complexity at late times is such an essential property of holographic complexity that the authors of [17,18] a few years after CV and CA prescriptions, proposed that every geometrical object in asymptotically Anti-de Sitter space-time which has linear growth (and also reproduce the switch-back effect in shock wave geometries) is gravitational dual of complexity. 2 A leading arena for the investigation of holographic complexity is the two-sided eternal BTZ black hole which is also our motivation for the present paper.…”
Section: Jhep04(2023)076mentioning
confidence: 99%
“…Three main conjectures have been put forward for the holographic dual of complexity: complexity = volume (CV) [44], relating complexity to the volume of codimensionone extremal surfaces, complexity = action (CA) [45,46], invoking the full gravitational action of the Wheeler-DeWitt (WDW) patch, and CV 2.0 [47], involving the spacetime volume of the WDW patch. Recently, it has been pointed out that an infinite class of observables defined on codimension-one [48] and codimension-zero [49] bulk regions exist which grow linearly at late times in the classical regime and are subject to the switchback effect [42,50]. Such an arbitrariness in selecting the bulk counterpart of complexity may mirror the intrinsic ambiguity in the choice of elementary gates in the complexity definition.…”
Section: Introductionmentioning
confidence: 99%