Chaos, wormholes, and holography: A tale of topology in quantum gravity

van der Heijden, J.J.

Chaos, wormholes, and holography: A tale of topology in quantum gravity

J.J. van der Heijden
(
- Amsterdam U.
)

2023

290 pages

Supervisor:

E.P. Verlinde

Thesis: PhD

Amsterdam U.

(2023)

ISBN:

9789464695755

Published: 2023

URN/HDL:

11245.1/9e89726b-e477-4bfe-b661-df4528948963

links

reference search0 citations

Citations per year

0 Citations

Abstract: (Amsterdam U.)

Combining quantum mechanics and general relativity is one of the most important open problems in theoretical physics. A formalapproach towards quantizing gravity is given by the gravitational path integral. However, dealing with quantum fluctuationsof spacetime itself is in general a very complicated task. In this thesis, I therefore study a simple model of two-dimensionalgravity in Anti-de Sitter (AdS) space where it is possible to calculate exactly a class of such quantum fluctuations, so-calledEuclidean wormholes, which correspond to geometries with a non-trivial topology. This computation relies on the holographicprinciple: the idea that AdS gravity is dual to some microscopic quantum theory without gravity, a conformal field theory(CFT), that lives in one dimension less. Surprisingly, the non-trivial surfaces appear to contain important information aboutthis underlying quantum theory: They point to a deep connection between quantum gravity and quantum chaos. To be precise,the results of this thesis show that black holes in two-dimensional AdS space obey the rules of quantum chaos, and that therelevant quantum effects can be realized geometrically in the path integral. This is an important step towards understandingthe quantum nature of black holes. Finally, I study the role of geometric phases in the AdS/CFT correspondence, and show thatthe modular Berry phase in the CFT is holographically dual to a particular geometric quantity in the AdS space, the so-calledbulk symplectic form.More

References(290)

Figures(0)

[1]

A universe field theory for JT gravity

Boris Post
(
- Amsterdam U.
)
,
Jeremy van der Heijden
(
- Amsterdam U.
)
,
Erik Verlinde
(
- Amsterdam U.
)

- JHEP 05 (2022) 118
•
e-Print:
- 2201.08859
•
DOI:
- 10.1007/JHEP05(2022)118

[2]

Quantum chaos in 2D gravity

Alexander Altland
(
- Cologne U.
)
,
Boris Post
(
- Amsterdam U.
)
,
Julian Sonner
(
- U. Geneva (main)
)
,
Jeremy van der Heijden
(
- Amsterdam U.
)
,
Erik P. Verlinde
(
- Amsterdam U.
)

- SciPost Phys. 15 (2023) 2, 064,
- SciPost Phys. 15 (2023) 064
•
e-Print:
- 2204.07583
•
DOI:
- 10.21468/SciPostPhys.15.2.064

[3]

Virasoro entanglement Berry phases

Jan de Boer
(
- Amsterdam U.
)
,
Ricardo Espíndola
(
- Amsterdam U.
)
,
Bahman Najian
(
- Amsterdam U.
)
,
Dimitrios Patramanis
(
- Warsaw U.
)
,
Jeremy van der Heijden
(
- Amsterdam U.
)

et al.

- JHEP 03 (2022) 179
•
e-Print:
- 2111.05345
•
DOI:
- 10.1007/JHEP03(2022)179

[4]

Changing states in holography: From modular Berry curvature to the bulk symplectic form

Bartlomiej Czech
(
- Tsinghua U., Beijing
)
,
Jan de Boer
(
- Amsterdam U.
)
,
Ricardo Espíndola
(
- Tsinghua U., Beijing and
- Amsterdam U.
)
,
Bahman Najian
(
- Amsterdam U.
)
,
Jeremy van der Heijden
(
- Amsterdam U.
)

et al.

- Phys.Rev.D 108 (2023) 6, 066003
•
e-Print:
- 2305.16384
•
DOI:
- 10.1103/PhysRevD.108.066003

[5]

Black holes and the second law

J.D. Bekenstein
(
- Princeton U.
)

- Lett.Nuovo Cim. 4 (1972) 737-740
•
DOI:
- 10.1007/BF02757029

[6]

Black holes and entropy

Jacob D. Bekenstein
(
- Princeton U. and
- Texas U.
)

- Phys.Rev.D 7 (1973) 2333-2346
•
DOI:
- 10.1103/PhysRevD.7.2333

[7]

Gravitational radiation from colliding black holes

S.W. Hawking
(
- Cambridge U.
)

- Phys.Rev.Lett. 26 (1971) 1344-1346
•
DOI:
- 10.1103/PhysRevLett.26.1344

[8]

Black holes in general relativity

S.W. Hawking
(
- Cambridge U.
)

- Commun.Math.Phys. 25 (1972) 152-166
•
DOI:
- 10.1007/BF01877517

[9]

Reversible and irreversible transforations in black hole physics

D. Christodoulou
(
- Princeton U.
)

- Phys.Rev.Lett. 25 (1970) 1596-1597
•
DOI:
- 10.1103/PhysRevLett.25.1596

[10]

Reversible transformations of a charged black hole

- Phys.Rev.D 4 (1971) 3552-3555
•
DOI:
- 10.1103/PhysRevD.4.3552

[11]

The Four laws of black hole mechanics

- Commun.Math.Phys. 31 (1973) 161-170
•
DOI:
- 10.1007/BF01645742

[12]

Particle Creation by Black Holes

S.W. Hawking
(
- Cambridge U., DAMTP and
- Caltech
)

- Commun.Math.Phys. 43 (1975) 199-220,
- Commun.Math.Phys. 46 (1976) 206 (erratum),
•
DOI:
- 10.1007/BF02345020

[12]

Particle Creation by Black Holes

S.W. Hawking
(
- Cambridge U., DAMTP and
- Caltech
)

- Commun.Math.Phys. 43 (1975) 199-220,
- Commun.Math.Phys. 46 (1976) 206 (erratum),
•
DOI:
- 10.1007/BF02345020

[13]

Microscopic origin of the Bekenstein-Hawking entropy

Andrew Strominger
(
- UC, Santa Barbara
)
,
Cumrun Vafa
(
- Harvard U.
)

- Phys.Lett.B 379 (1996) 99-104
•
e-Print:
- hep-th/9601029
•
DOI:
- 10.1016/0370-2693(96)00345-0

[14]

Breakdown of Predictability in Gravitational Collapse

S.W. Hawking
(
- Cambridge U. and
- Caltech
)

- Phys.Rev.D 14 (1976) 2460-2473
•
DOI:
- 10.1103/PhysRevD.14.2460

[15]

Dimensional reduction in quantum gravity

Gerard 't Hooft
(
- Utrecht U.
)

- Conf.Proc.C 930308 (1993) 284-296
•
e-Print:
- gr-qc/9310026

[16]

The World as a hologram

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

- J.Math.Phys. 36 (1995) 6377-6396
•
e-Print:
- hep-th/9409089
•
DOI:
- 10.1063/1.531249

[17]

The Large N limit of superconformal field theories and supergravity

Juan Martin Maldacena
(
- Harvard U.
)

- Int.J.Theor.Phys. 38 (1999) 1113-1133 (reprint),
- Adv.Theor.Math.Phys. 2 (1998) 231-252
•
e-Print:
- hep-th/9711200
•
DOI:
- 10.4310/ATMP.1998.v2.n2.a1