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Entanglement interpretation of black hole entropy in string theoryPowerPoint Presentation

Entanglement interpretation of black hole entropy in string theory

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### Entanglement interpretation of black hole entropy in string theory

Amos Yarom.

Ram Brustein.

Martin Einhorn.

What is entanglement entropy? theory

What does BH entropy mean?- BH Microstates
- Entanglement entropy
- Horizon states

How does it relate to BH entropy?

How does string theory evaluate BH entropy?

How are these two methods relate to each other?

All |↓ theory22↓|

elements

1

2

Entanglement entropyS=0

S1=Trace (r1lnr1)=ln2

S2=Trace (r2lnr2)=ln2

Tr theoryin(y’ y’’

rout(y’1,y’’1) =

Exp[-SE] DfD2

f(x,0+)=y’(x)

f(x,0)=y(x)

f(x,0+)=y’(x)

f(x,0-)=y’’(x)

t

f(x,0-)=y’’(x)

out y’1 y’’1 Exp[-SE] Df

f(x,0+) = y’1(x)y2(x)

y’(x)

y’’(x)

f(x,0-) = y’’1(x)y2(x)

x

f(x,0+) = y’1(x)

f(x,0-) = y’’1(x)

Finding rout

Kabat & Strassler (1994), R. Brustein, M. Einhorn and A.Y. (2005)

t theory

out y’1 y’’1 Exp[-SE] Df

y’1(x)

x

y’’1(x)

f(x,0+) = y’1(x)

f(x,0-) = y’’1(x)

Finding rin

Kabat & Strassler (1994), R. Brustein, M. Einhorn and A.Y. (2005)

’| e-bH|’’

b=T-1=f ’(r0)/4p

BTZ BH theory

What is entanglement entropy? theory

What is entanglement entropy of BH’s

How does string theory evaluate BH entropy?

How are these two methods relate to each other?

Black hole entanglement entropy

S.P. de Alwis, N. Ohta, (1995)

? theory

How to relate them? theory

Anti deSitter

+BH

CFT

What is entanglement entropy?

What is entanglement entropy of BH’s

How does string theory evaluate BH entropy?

AdS/CFT

How are these two methods relate to each other?

S/A

1/R

Free theory:

l 0

Semiclassical gravity:

R>>ls

AdS BH EntropyS. S. Gubser, I. R. Klebanov, and A. W. Peet (1996)

, T>0

S=A/3

SBH=A/4

How to relate them? theory

?

Thermofield doubles theoryTakahashi and Umezawa, (1975)

? theory

How to relate them?Dualities theory

R. Brustein, M. Einhorn and A.Y. (2005)

General picture theory

t theory

q

r

Explicit construction: BTZ BHMaldacena and Strominger (1998), Marolf and Louko (1998), Maldacena (2003)

Example: AdS BH’s theory

Area scaling of correlation functions theory

EE = V V E(x) E(y) ddx ddy

= V V FE(|x-y|) ddx ddy

= D(x) FE(x) dx

= D(x) 2g(x) dx

= - ∂x(D(x)/xd-1) xd-1 ∂xg(x) dx

Geometric term:

Operator dependent term

D(x)=V V d(xxy) ddx ddy

Geometric term theory

D(x)= V V d(xxy) ddx ddy

D(x)= d(xr) ddr ddR

ddR V + Ax +O(x2)

d(xr) ddr xd-1 +O(xd)

D(x)=C1Vxd-1 ± C2 Axd + O(xd+1)

Area scaling of correlation functions theory

EE = V V E(x) E(y) ddx ddy

= V1 V2 FE(|x-y|) ddx ddy

= D(x) FE(x) dx

= D(x) 2g(x) dx

= - ∂x(D(x)/xd-1) xd-1 ∂xg(x) dx

UV cuttoff at x~1/L

∂ x(D(x)/xd-1) 1/L

A

D(x)=C1Vxd-1 + C2 Axd + O(xd+1)

Consequences theory

R. Brustein M. Einhorn and A.Y. (in progress)

Summary theory

- BH entropy is a result of:
- Entanglement
- Microstates

- Counting of states using dual FT’s is consistent with entanglement entropy.

End theory

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