The boundary dual of the bulk symplectic form

Belin, Alexandre; Lewkowycz, Aitor; Sárosi, Gábor

doi:10.1016/j.physletb.2018.10.071

The boundary dual of the bulk symplectic form

Alexandre Belin
(
- Amsterdam U.
)
,
Aitor Lewkowycz
(
- Stanford U., Phys. Dept.
)
,
Gábor Sárosi
(
- Pennsylvania U. and
- Vrije U., Brussels
)

Jun 26, 2018

5 pages

Published in:

Phys.Lett.B 789 (2019) 71-75

Published: Feb 10, 2019

e-Print:

1806.10144 [hep-th]

DOI:

10.1016/j.physletb.2018.10.071 (publication)

View in:

reference search78 citations

Citations per year

Abstract: (Elsevier)

In this paper, we study the overlaps of wavefunctionals prepared by turning on sources in the Euclidean path integral. For nearby states, these overlaps give rise to a Kähler structure on the space of sources, which is naturally induced by the Fubini–Study metric. The Kähler form obtained this way can also be thought of as a Berry curvature and, for holographic field theories, we show that it is identical to the gravitational symplectic form in the bulk. We discuss some possible applications of this observation, in particular a boundary prescription to calculate the variation of the volume of a maximal slice.

Note:

6 pages, 1 figure, v2: published version

path integral: Euclidean
symplectic
overlap
potential: Kaehler
gravitation
duality: holography
field theory
topology

References(23)

Figures(1)

[1]

Holographic derivation of entanglement entropy from AdS/CFT

- Phys.Rev.Lett. 96 (2006) 181602
•
e-Print:
- hep-th/0603001
•
DOI:
- 10.1103/PhysRevLett.96.181602

[3]

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

[4]

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

[5]

Distance between Quantum States and Gauge-Gravity Duality

- Phys.Rev.Lett. 115 (2015) 26, 261602
•
e-Print:
- 1507.07555
•
DOI:
- 10.1103/PhysRevLett.115.261602

[6]

Relative entropy equals bulk relative entropy

Daniel L. Jafferis
(
- Harvard U., Phys. Dept.
)
,
Aitor Lewkowycz
(
- Princeton U.
)
,
Juan Maldacena
(
- Princeton, Inst. Advanced Study
)
,
S. Josephine Suh
(
- Santa Barbara, KITP and
- British Columbia U.
)

- JHEP 06 (2016) 004
•
e-Print:
- 1512.06431
•
DOI:
- 10.1007/JHEP06(2016)004

[7]

Complexity and the bulk volume, a new York time story

Alexandre Belin
(
- Amsterdam U.
)
,
Aitor Lewkowycz
(
- Stanford U., ITP
)
,
Gábor Sárosi
(
)

- JHEP 03 (2019) 044
•
e-Print:
- 1811.03097
•
DOI:
- 10.1007/JHEP03(2019)044

[8]

Quantal phase factors accompanying adiabatic changes

Michael V. Berry
(
- Bristol U.
)

- Proc.Roy.Soc.Lond.A 392 (1984) 45-57
•
DOI:
- 10.1098/rspa.1984.0023

[9]

Anti-de Sitter space and holography

Edward Witten
(
- Princeton, Inst. Advanced Study
)

- Adv.Theor.Math.Phys. 2 (1998) 253-291
•
e-Print:
- hep-th/9802150
•
DOI:
- 10.4310/ATMP.1998.v2.n2.a2

[10]

Real-time gauge/gravity duality: Prescription, Renormalization and Examples

Kostas Skenderis
(
- Amsterdam U.
)
,
Balt C. van Rees
(
- Amsterdam U.
)

- JHEP 05 (2009) 085
•
e-Print:
- 0812.2909
•
DOI:
- 10.1088/1126-6708/2009/05/085

[11]

On excited states in real-time AdS/CFT

Marcelo Botta-Cantcheff
(
- La Plata U.
)
,
Pedro Martínez
(
- La Plata U.
)
,
Guillermo A. Silva
(
- La Plata U.
)

- JHEP 02 (2016) 171
•
e-Print:
- 1512.07850
•
DOI:
- 10.1007/JHEP02(2016)171

[12]

From Euclidean Sources to Lorentzian Spacetimes in Holographic Conformal Field Theories

Marolf
,
Donald
,
Parrikar
,
Onkar
,
Rabideau

et al.

[13]

Irreversibility of the Flux of the Renormalization Group in a 2D Field Theory

A.B. Zamolodchikov
(
- Moscow, ITEP
)

- JETP Lett. 43 (1986) 730-732,
- Pisma Zh.Eksp.Teor.Fiz. 43 (1986) 565-567

[14]

Observations on the Moduli Space of Superconformal Field Theories

Nathan Seiberg
(
- Princeton, Inst. Advanced Study
)

- Nucl.Phys.B 303 (1988) 286-304
•
DOI:
- 10.1016/0550-3213(88)90183-6

[15]

Symplectic Geometry of the Covariant Phase Space, Superstrings and Superspace

Cedomir Crnkovic
(
- Princeton U.
)

- Class.Quant.Grav. 5 (1988) 1557-1575,
- CLASS. QUANTUM GRAV. 5 (1988) 1557-1575 AND PRINCETON UNIV. - PUPT-1059 (87,REC.AUG.) 38p
•
DOI:
- 10.1088/0264-9381/5/12/008