diving into traversable wormholes - particle …journal/jc2017_slides/...if we through matter with...

Diving into Traversable Wormholes

Journal Club@Osaka University July 26, 2017

Tokiro Numasawa

Osaka University Particle Physics TheoryBased on arXiv:1704.05333 J. Maldacena, D.Stanford and Z. Yang

see also “Traversable Wormholes via a Double Trace Deformation” arXiv:1608.05687, P. Gao , D.Jafferis and A.Wall (Iizuka-san’s JC)

“Conformal symmetry and its breaking in two dimensional Nearly Anti de-Sitter space” arXiv:1606.01857 J. Maldacena, D.Stanford and Z. Yang

2

This paper talks about…

・Traversable wormholes in Nearly AdS2 gravity・Application to information problems

3

This paper talks about…

・Traversable wormholes in Nearly AdS2 gravity・Application to information problems

(1)Introduction/Review of traversable wormholes (2)Nearly AdS2 gravity(3)Traversable wormholes in Nearly AdS2 gravity(4)Application to information problem (5)Conclusion

4

Horizonis described

https://www.sciencenews.org/blog/context/new-einstein-equation-wormholes-quantum-gravity

1.Introduction

by


HorizonMatter

Realistic Black Holes are created by collapsing matters.

1.Introduction

Horizon BH

4d Schwarzschild: ds2 = �(1� 2M

r)dt2 +

1

1� 2Mr

dr2 + r2d⌦22


1.Introduction

Horizon


BH

But Einstein eq. also permits eternal Black holes solutions:

Horizon

4d Schwarzschild: ds2 = �(1� 2M

r)dt2 +

1

1� 2Mr

dr2 + r2d⌦22

ds2 = �32M3

re�

r2M dUdV + r2d⌦2

2

:just a coordinate transformation

1.Introduction

HorizonThis approximately describes



Horizon

time slice

Einstein-Rosen Bridge(Wormhole)

1.Introduction

Horizon

time slice

https://ja.wikipedia.org/wiki/ブラックホール


1.Introduction

https://ja.wikipedia.org/wiki/

Horizon

time slice


1.Introduction

Horizon

Einstein-Rosen bridge

time slice

Can we go to the other side?

1.Introduction

Horizon

Einstein-Rosen bridge

time slice

Can we go to the other side?

→No.

1.Introduction

If we through matter with negative energy(violate Averaged Null Energy Condition)

BH

If we through matter with negative energy(violate Averaged Null Energy Condition)

BH

→He can escape from Black Holeshorizon radius decreases

Traversable wormhole via double trace deformation[Gao-Jefferis-Wall, 16]

CFTL CFTR・CFTL and CFTR are decoupled:

H = HL +HR

・Assume　AdS/CFT


CFTL CFTR・CFTL and CFTR are decoupled

・States are entangled|TFDi = 1p

Z(�)

X

n

e�2 En |EniL ⌦ |EniR

H = HL +HR

・Assume　AdS/CFT




Z(�)

X

n


H = HL +HR

to obtain traversability…・put interaction term Hint = g

Z t+�t

tOL(t)OR(t)

・Assume　AdS/CFT




Z(�)

X

n


H = HL +HR

to obtain traversability…・put interaction term Hint = g

Z t+�t

tOL(t)OR(t)

・effectively compactly radial direction to circle →negative energy by Casimir effect

・Assume　AdS/CFT

(positive/negative depend on the sign of g)


24

2.Nearly AdS2 gravity dynamics

・exact AdS2 does not permit finite energy excitation

For example, → Tµ⌫ = 0Z

pgR+ Smatter

Horizon

AdS2 ⇥ Y UV geometry


・But AdS2 × Y type geometry appears from near horizon limit of near extremal BHs


pgR+ Smatter



・But AdS2 × Y type geometry appears from near horizon limit of near extremal BHs


pgR+ Smatter

Horizon

AdS2 ⇥ Y UV geometry

・middle geometry can be changed by finite energy excitation


Horizon

AdS2

・Consider a model of following part.

Horizon

AdS2

AdS2 boundary


→AdS2 are cut at some trajectory in AdS2.

→ include the term that perturb from AdS21

16⇡G

Z�pg(R+ 2) +

1

8⇡G

Z

bdy�bK

Horizon

AdS2

AdS2 boundary

・We want to include the effect of finite energy excitation

[Almheiri-Polchinski 14][Jackiw 85][Teitelboim 83]



→ include the term that perturb from AdS21

16⇡G

Z�pg(R+ 2) +

1

8⇡G

Z

bdy�bK

Horizon

AdS2


AdS2 boundary

・We want to include the effect of finite energy excitation

・We call this nearly AdS2 gravity

[Almheiri-Polchinski 14][Jackiw 85][Teitelboim 83]


Nearly AdS2 gravity

S = �C

Zdu{f(u), u}

{f(u), u} =f 000

f 0 � 3

2

⇣f 00

f 0

⌘2

Schwarzian action:

describes the dynamics of boundary cutoff curveDynamics are encoded the motion of boundary curve !

1

16⇡G

Z�pg(R+ 2) +

1

8⇡G

Z

bdy�bK

SYK model (1d Nearly CFT)

Nearly AdS2 gravity

S = �C

Zdu{f(u), u}

{f(u), u} =f 000

f 0 � 3

2

⇣f 00

f 0

⌘2

Schwarzian action:

describes the dynamics of boundary cutoff curveDynamics are encoded the motion of boundary curve !

low energy

1

16⇡G

Z�pg(R+ 2) +

1

8⇡G

Z

bdy�bK


34

BH solution

cutoff curve in global AdS2 (described by Schwarzian action)

Horizon

(BH/Rindler patch)

3.Traversable wormhole in Nearly AdS2

What we need is to see the dynamics ofboundary curves

not traversable

BH solution

eig�L(tL)�R(tR)

eigh�L(tL)�R(tR)i

⇠ e�igVpot

Vpot

⇠ e�m⇢

⇢ :AdS distance

put two side interaction

eig�L(tL)�R(tR)


⇠ e�igVpot

Vpot

⇠ e�m⇢

⇢ :AdS distance

pushed

g > 0: attractive force (wormhole becomes traversable)

:Approximate

eig�L(tL)�R(tR)


⇠ e�igVpot

:Approximate

g > 0: attractive force (wormhole becomes traversable)

Vpot

⇠ e�m⇢

⇢ :AdS distance

pushed

eig�L(tL)�R(tR)


⇠ e�igVpot

:Approximate

g > 0: attractive force (wormhole becomes traversable)g < 0: repulsive force (not traversable)

Vpot

⇠ e�m⇢

⇢ :AdS distance

Back reaction

Back reaction

kicked outward

Back reaction

Vpot

⇠ e�m⇢

⇢ :AdS distance→becomes long by back reaction


45

4.Application to information problem

Problem: Can we extract the information behind the horizon from Hawking radiations?

[Hayden-Preskill,07]


BH

Consider one side BH

Bob

Horizon


BH

Horizon


Bob

Bob collects Hawking radiations (entangled with BH)…


BH


Bob

After half evaporation…

Horizon


BH


Bob


Bob create 2nd BH by radiations

BH

Horizon




Bob


Assume EPR=ER (entanglement = wormhole) [Maldacena-Susskind,13]

Horizon

Bob create 2nd BH by radiations

BHBH



Then, we obtain

Bob

BHoriginal BH

Bob’s 2nd BH

connected by a wormhole

BH2


Then, we obtain

Bob

BH

Now, Alice throws her message in the original BH

Alice

BH2 Bob’s 2nd BH

original BH



Then, we obtain

Bob

BH

Now, Alice throws her message in the original BH

Alice

BH2

By traversable wormhole protocol, Bob can extract Alice’s message from radiations(2nd BH)

Bob’s 2nd BH

original BH




56

・They studied traversability of wormholes in nearly AdS2 gravity

・Because of the simple dynamics in nearly AdS2 gravity,we can also see the back reaction of message.

・Assuming ER=EPR, traversable wormholes are used to extract information behind the horizon from Hawking radiations

5.Conclusion

Appendix

Averaged Null Energy Condition(ANEC) and Traversability

ds2 = �r2 � r2hl2

dt2 +l2

r2 � r2hdr2 + r2d⌦2

d�2BH metric:

After perturbation , satisfiesTµ⌫ ⇠ O(✏) hµ⌫ = �gµ⌫ ⇠ O(✏)

d� 2

4[(d� 3)r�2

h +(d� 1)l�2(hUU +@U (UhUU ))� 2r�2h @2

Uh��] = 8⇡GNTUU

at V = 0 in Kruskal Coordinate

V (U) = �(2gUV (0))

Z U

�1dU hUU

8⇡GN

ZdUTUU =

d� 2

4((d� 3)r�2

h + (d� 1)l�2)

ZdUhUU

→ANEC = traversability

AdS2 form Higher dim

・Magnetic brane

ds

24 = gµ⌫dx

µdx

⌫ + �2(x)(dy21 + dy

22)

L =1

16⇡GN

p�g�2R+ �(r�)2 � U(�)

・CGHS modelU(�) = �A�2� = 4

UV: near extremal diatonic BH at 4 or 5 dim

UV:

� = 2 U(�) =B

�2�A�2

| iA ⌦ |EPRiBC

Initial state:Quantum Teleportation

=1

2

4X

k=1

| kiAB ⌦ | ki

| i = ↵ |0i+ � |1i

| 1i =1p2(|0i |1i � |1i |0i) | 2i =

1p2(|0i |1i+ |1i |0i)

| 3i =1p2(|0i |0i � |1i |1i) | 4i =

1p2(|0i |0i+ |1i |1i)

| 1i = ↵ |1i � � |0i | 2i = ↵ |1i+ � |0i

| 3i = ↵ |0i � � |1i | 4i = ↵ |0i+ � |1i

where

Pk = | ki h k|Projection: ,

Alice Bob Charlie

EPR state

| i

Projection Measurement

Classical Comm.

| ki

Uk

Unitary Transf.

| i

X

k

Pk = 1

Uk : k dependent Unitary (indep. from α and β )61

[cf: Bennett-Brassard-Crepeau-Jozsa-Peres-Wootters 93]

CFT1

Conformal symmetry → Tµµ = 0

In 1d , and there are no finite energy excitation

T 00 = H = 0

In 1d, QFT becomes quantum mechanics

diving into traversable wormholes - particle …journal/jc2017_slides/...if we through matter with...

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