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A. Bernamonti, F. Galli, J. Hernandez, R. C. Myers, S.-M. Ruan, and J. Simón, First Law of Holographic Complexity, Phys. Rev. Lett. 123
Original
1903
Earlier work this paper cites.
M. Flory, Discrete Scale Invariance in Holography and an Argument Against the Complexity = Action Proposal, Acta Phys. Polon. Supp. 13
Original
1912
Earlier work this paper cites.
R. E. Peierls, The Commutation laws of relativistic field theory, Proc. Roy. Soc. Lond. A 214
1952
Earlier work this paper cites.
K. Sfetsos, On gravitational shock waves in curved space-times, Nucl. Phys. B 436
1995
Earlier work this paper cites.
A. Belin and B. Withers, From sources to initial data and back again: on bulk singularities in Euclidean AdS/CFT, JHEP 12
Original
2007
Earlier work this paper cites.
J. Hernandez, R. C. Myers, and S.-M. Ruan, Quantum extremal islands made easy. Part III. Complexity on the brane, JHEP 02
Original
2010
Earlier work this paper cites.

Similar

D. Stanford and L. Susskind, Complexity and Shock Wave Geometries, Phys. Rev. D 90
Original
2014
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M. Alishahiha, Holographic Complexity, Phys. Rev. D 92
Original
2015
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L. Susskind, Computational Complexity and Black Hole Horizons, Fortsch. Phys. 64
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2016
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A. R. Brown, D. A. Roberts, L. Susskind, B. Swingle, and Y. Zhao, Holographic Complexity Equals Bulk Action?, Phys. Rev. Lett. 116
Original
2016
Cited alongside, same era.
L. Lehner, R. C. Myers, E. Poisson, and R. D. Sorkin, Gravitational action with null boundaries, Phys. Rev. D 94
Original

Then

P. Bueno, V. S. Min, A. J. Speranza, and M. R. Visser, Entanglement equilibrium for higher order gravity, Phys. Rev. D 95
Original
2017
Later among the works it cites.
E. Witten, Canonical quantization in anti de sitter space, in PCTS (2017)
2017
Later among the works it cites.
L. V. Iliesiu, M. Mezei, and G. Sárosi, The volume of the black hole interior at late times, (2021), arXiv:2107.06286 [hep-th]
Original
2021
Closest in time.
N. Engelhardt and r. Folkestad, General Bounds on Holographic Complexity, (2021), arXiv:2109.06883 [hep-th]
Original
2021
Closest in time.
A. Belin, R. C. Myers, S.-M. Ruan, G. Sárosi, and A. J. Speranza, in preparation (2022)
2022
Closest in time.

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2021

Does Complexity Equal Anything?

Belin, Alexandre, Myers, Robert C., Ruan, Shan-Ming et al.

Understand

We present a new infinite class of gravitational observables in asymptotically Anti-de Sitter space living on codimension-one slices of the geometry, the most famous of which is the volume of the maximal slice.

We show that these observables display universal features for the thermofield-double state: they grow linearly in time at late times and reproduce the switch-back effect in shock wave geometries.
We argue that any member of this class of observables is an equally viable candidate as the extremal volume for a gravitational dual of complexity.

Built on

A. Bernamonti, F. Galli, J. Hernandez, R. C. Myers, S.-M. Ruan, and J. Simón, First Law of Holographic Complexity, Phys. Rev. Lett. 123
Original
1903
Earlier work this paper cites.
M. Flory, Discrete Scale Invariance in Holography and an Argument Against the Complexity = Action Proposal, Acta Phys. Polon. Supp. 13
Original
1912
Earlier work this paper cites.
R. E. Peierls, The Commutation laws of relativistic field theory, Proc. Roy. Soc. Lond. A 214
1952
Earlier work this paper cites.
K. Sfetsos, On gravitational shock waves in curved space-times, Nucl. Phys. B 436
1995
Earlier work this paper cites.
A. Belin and B. Withers, From sources to initial data and back again: on bulk singularities in Euclidean AdS/CFT, JHEP 12
Original
2007
Earlier work this paper cites.
J. Hernandez, R. C. Myers, and S.-M. Ruan, Quantum extremal islands made easy. Part III. Complexity on the brane, JHEP 02
Original
2010
Earlier work this paper cites.

Similar

D. Stanford and L. Susskind, Complexity and Shock Wave Geometries, Phys. Rev. D 90
Original
2014
Cited alongside, same era.
M. Alishahiha, Holographic Complexity, Phys. Rev. D 92
Original
2015
Cited alongside, same era.
L. Susskind, Computational Complexity and Black Hole Horizons, Fortsch. Phys. 64
Original
2016
Cited alongside, same era.
A. R. Brown, D. A. Roberts, L. Susskind, B. Swingle, and Y. Zhao, Holographic Complexity Equals Bulk Action?, Phys. Rev. Lett. 116
Original
2016
Cited alongside, same era.
L. Lehner, R. C. Myers, E. Poisson, and R. D. Sorkin, Gravitational action with null boundaries, Phys. Rev. D 94
Original

Then

P. Bueno, V. S. Min, A. J. Speranza, and M. R. Visser, Entanglement equilibrium for higher order gravity, Phys. Rev. D 95
Original
2017
Later among the works it cites.
E. Witten, Canonical quantization in anti de sitter space, in PCTS (2017)
2017
Later among the works it cites.
L. V. Iliesiu, M. Mezei, and G. Sárosi, The volume of the black hole interior at late times, (2021), arXiv:2107.06286 [hep-th]
Original
2021
Closest in time.
N. Engelhardt and r. Folkestad, General Bounds on Holographic Complexity, (2021), arXiv:2109.06883 [hep-th]
Original
2021
Closest in time.
A. Belin, R. C. Myers, S.-M. Ruan, G. Sárosi, and A. J. Speranza, in preparation (2022)
2022
Closest in time.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

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2016

Cited alongside, same era.

T. Hartman and J. Maldacena, Time Evolution of Entanglement Entropy from Black Hole Interiors, JHEP 05

Original

Cited in the paper.

J. Couch, W. Fischler, and P. H. Nguyen, Noether charge, black hole volume, and complexity, JHEP 03

Original

Cited in the paper.

See Supplemental Material (appendix A) for a detailed analysis involving a Weyl-squared term C μ ν ρ σ C μ ν ρ σ C_{\mu\nu\rho\sigma}C^{\mu\nu\rho\sigma}

Cited in the paper.

D. Carmi, S. Chapman, H. Marrochio, R. C. Myers, and S. Sugishita, On the Time Dependence of Holographic Complexity, JHEP 11

Original

Cited in the paper.

S. Chapman, H. Marrochio, and R. C. Myers, Holographic complexity in Vaidya spacetimes. Part II, JHEP 06

Original

Cited in the paper.

We note that the integrand is divergent at the horizon because f ⁡ ( r ) ∼ f ′ ( r h ) ( r − r h ) f(r)\sim f^{\prime}(r_{h})(r-r_{h}) . Hence this integral ( 14

Cited in the paper.

This result relies on having a scale invariant planar horizon, corresponding to a thermodynamic limit in the CFT. For compact horizons, there are finite size corrections, just like in the case of the CV proposal [ 11 ]

Cited in the paper.