Does Complexity Equal Anything?

Belin, Alexandre; Myers, Robert C.; Ruan, Shan-Ming; Sárosi, Gábor; Speranza, Antony J.

doi:10.1103/PhysRevLett.128.081602

Does Complexity Equal Anything?

Alexandre Belin
(
- CERN
)
,
Robert C. Myers
(
- Perimeter Inst. Theor. Phys.
)
,
Shan-Ming Ruan
(
)
,
Gábor Sárosi
(
- CERN
)
,
Antony J. Speranza
(
- Perimeter Inst. Theor. Phys. and
- Illinois U., Urbana
)

Nov 3, 2021

7 pages

Published in:

Phys.Rev.Lett. 128 (2022) 8, 081602

Published: Feb 23, 2022

e-Print:

2111.02429 [hep-th]

DOI:

10.1103/PhysRevLett.128.081602 (publication)

Report number:

CERN-TH-2021-181,
YITP-22-02

View in:

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Abstract: (APS)

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.

Note:

6 pages + appendices, 3 figures; v2 minor edits and title change - version as in PRL

gravitation: duality
space: anti-de Sitter
horizon: geometry
black hole
field theory: conformal
holography
diffeomorphism: invariance

References(28)

Figures(4)

Seminars

[1]

Time Evolution of Entanglement Entropy from Black Hole Interiors

- JHEP 05 (2013) 014
•
e-Print:
- 1303.1080
•
DOI:
- 10.1007/JHEP05(2013)014

[2]

Computational Complexity and Black Hole Horizons

Leonard Susskind
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)

- Fortsch.Phys. 64 (2016) 44-48 (addendum),
- Fortsch.Phys. 64 (2016) 24-43
•
e-Print:
- 1403.5695
•
DOI:
- 10.1002/prop.201500092

[2]

Computational Complexity and Black Hole Horizons

Leonard Susskind
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)

- Fortsch.Phys. 64 (2016) 44-48 (addendum),
- Fortsch.Phys. 64 (2016) 24-43
•
e-Print:
- 1403.5695
•
DOI:
- 10.1002/prop.201500092

[3]

Holographic Complexity Equals Bulk Action?

Adam R. Brown
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)
,
Daniel A. Roberts
(
- MIT, Cambridge, CTP and
- MIT, LNS
)
,
Leonard Susskind
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)
,
Brian Swingle
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)
,
Ying Zhao
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)

- Phys.Rev.Lett. 116 (2016) 19, 191301
•
e-Print:
- 1509.07876
•
DOI:
- 10.1103/PhysRevLett.116.191301

[4]

Noether charge, black hole volume, and complexity

Josiah Couch
(
- Texas U. and
- Texas U., TCC
)
,
Willy Fischler
(
- Texas U. and
- Texas U., TCC
)
,
Phuc H. Nguyen
(
- Texas U. and
- Texas U., TCC
)

- JHEP 03 (2017) 119
•
e-Print:
- 1610.02038
•
DOI:
- 10.1007/JHEP03(2017)119

[5]

Gravitational action with null boundaries

- Phys.Rev.D 94 (2016) 8, 084046
•
e-Print:
- 1609.00207
•
DOI:
- 10.1103/PhysRevD.94.084046

[6]

Holographic Complexity

Mohsen Alishahiha
(
- IPM, Tehran
)

- Phys.Rev.D 92 (2015) 12, 126009
•
e-Print:
- 1509.06614
•
DOI:
- 10.1103/PhysRevD.92.126009

[7]

Entanglement equilibrium for higher order gravity

Pablo Bueno
(
- Amsterdam U. and
- Leuven U.
)
,
Vincent S. Min
(
- Leuven U.
)
,
Antony J. Speranza
(
- Maryland U.
)
,
Manus R. Visser
(
- Amsterdam U.
)

- Phys.Rev.D 95 (2017) 4, 046003
•
e-Print:
- 1612.04374
•
DOI:
- 10.1103/PhysRevD.95.046003

[8]

Quantum extremal islands made easy. Part III. Complexity on the brane

Juan Hernandez
(
- Perimeter Inst. Theor. Phys. and
- Waterloo U.
)
,
Robert C. Myers
(
- Perimeter Inst. Theor. Phys.
)
,
Shan-Ming Ruan
(
- Perimeter Inst. Theor. Phys. and
- Waterloo U.
)

- JHEP 02 (2021) 173
•
e-Print:
- 2010.16398
•
DOI:
- 10.1007/JHEP02(2021)173

[9]

Complexity and Shock Wave Geometries

Douglas Stanford
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)
,
Leonard Susskind
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)

- Phys.Rev.D 90 (2014) 12, 126007
•
e-Print:
- 1406.2678
•
DOI:
- 10.1103/PhysRevD.90.126007

[10]

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 [26]

[11]

Multiple Shocks

Stephen H. Shenker
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)
,
Douglas Stanford
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)

- JHEP 12 (2014) 046
•
e-Print:
- 1312.3296
•
DOI:
- 10.1007/JHEP12(2014)046

[12]

On gravitational shock waves in curved space-times

Konstadinos Sfetsos
(
- Utrecht U.
)

- Nucl.Phys.B 436 (1995) 721-745
•
e-Print:
- hep-th/9408169
•
DOI:
- 10.1016/0550-3213(94)00573-W

[13]

Clearly, this result will also hold for more general stationary spacetimes, e.g., black holes with spherical or hyperbolic horizons. One can view this as a generalization of a similar result [27] for AdS shockwaves to static Kruskal geometries

[14]

More on complexity equals anything, in preparation