Download presentation

Presentation is loading. Please wait.

Published byHarold Dolph Modified over 2 years ago

1
Area scaling from entanglement in flat space quantum field theory Introduction Area scaling of quantum fluctuations Unruh radiation and Holography

2
Black hole thermodynamics J. Beckenstein (1973) S. Hawking (1975) S A THTH S = ¼ A

3
An ‘artificial’ horizon. V V in out

4
Entropy: S in =Tr( in ln in ) S in =S out Srednicki (1993)

5
Entanglement entropy of a sphere out in Entropy R2R2 Srednicki (1993)

6
Other Thermodynamic quantities Heat capacity: More generally: A ? ?

7
A different viewpoint in out = No accessRestricted measurements

8
Area scaling of fluctuations R. Brustein and A.Y., (2004) O a V1 O b V2 V1V1 Assumptions: V2V2 O a V1 2

9
Area scaling of correlation functions O a V1 O b V2 = V1 V2 O a (x) O b (y) d d x d d y = V1 V2 F ab (|x-y|) d d x d d y = D( ) F ab ( ) d D( )= V V ( x y ) d d x d d y Geometric term: Operator dependent term = D( ) 2 g( ) d = - ∂ (D( )/ d-1 ) d-1 ∂ g( ) d

10
Geometric term D( )= V1 V2 ( x y ) d d x d d y V1V1 V2V2 = ( r) d d r d d R d d R A 2 ) ( r) d d r d-1 +O( d ) D( )=C 2 A d + O( d+1 )

11
Geometric term D( )= ( r) d d r d d R d d R V + A 2 ) ( r) d d r d-1 +O( d ) D( )=C 1 V d-1 ± C 2 A d + O( d+1 ) V 1 =V 2

12
Area scaling of correlation functions O a V1 O b V2 = V1 V2 O a (x) O b (y) d d x d d y = V1 V2 F ab (|x-y|) d d x d d y = D( ) F ab ( ) d = D( ) 2 g( ) d ∂ (D( )/ d-1 ) = - ∂ (D( )/ d-1 ) d-1 ∂ g( ) d UV cuttoff at ~1/ D( )=C 1 V d-1 + C 2 A d + O( d+1 ) A

13
Energy fluctuations

14
Intermediate summary V V Tr( in O V ) Tr( in O V 2 )

15
Finding in (x,0)= (x) x t ’(x) ’’(x) Tr out ( ’ ’’ in ( ’ in, ’’ in ) = in ’ in ’’ in Exp[-S E ] D (x,0 + ) = ’ in (x) (x,0 - ) = ’’ in (x) (x,0 + ) = ’ in (x) out (x) (x,0 - ) = ’’ in (x) out (x) Exp[-S E ] D D out ’’ in (x) ’ in (x) (x,0 + )= ’(x) (x,0 - )= ’’(x) (x,0 + )= ’(x) (x,0 - )= ’’(x)

16
Finding rho x t ’ in (x) ’’ in (x) in ’ in ’’ in Exp[-S E ] D (x,0 + ) = ’ in (x) (x,0 - ) = ’’ in (x) ’| e - K | ’’ Kabbat & Strassler (1994)

17
Rindler space (Rindler 1966) ds 2 = -dt 2 +dx 2 + dx i 2 ds 2 = -a 2 2 d 2 +d 2 + dx i 2 t= /a sinh(a ) x= /a cosh(a ) Acceleration = a/ Proper time = x t = const =const H R = K x

18
Unruh Radiation (Unruh, 1976) x t ds 2 = -a 2 2 d 2 +d 2 + dx i 2 = 0 a ≈ a +i2 Avoid a conical singularity Periodicity of Greens functions Radiation at temperature 0 = 2 /a R = e - H R = e - K = in

19
Schematic picture VEVs in V of Minkowski space VV Observer in Minkowski space with d.o.f restricted to V Canonical ensemble in Rindler space (if V is half of space) Tr( in O V ) = Tr( R O V ) =

20
Other shapes R. Brustein and A.Y., (2003) in ’ in ’’ in Exp[-S E ] D (x,0 + ) = ’ in (x) (x,0 - ) = ’’ in (x) x t ’’ in( x) ’ in( x) = ’ in |e - H 0 | ’’ out d/dt H 0 = 0 S E = 0 H 0 dt (x,t), (x,t), +B.C. H 0 =K, in={x|x>0}

21
Evidence for bulk-boundary correspondence V1V1 O V1 O V2 A 1 A 2 OV1OV2OV1OV2 V2V2 OV1OV2OV1OV2 V1 V2 V1 V2 O V1 O V2 - O V 1 O V2 Pos. of V 2 R. Brustein D. Oaknin, and A.Y., (2003)

22
A working example Large N limit R. Brustein and A.Y., (2003)

23
Summary V Area scaling of Fluctuations due to entanglement Unruh radiation and Area dependent thermodynamics A Boundary theory for fluctuations Statistical ensemble due to restriction of d.o.f V A Minkowski observer restricted to part of space will observe: Radiation. Area scaling of thermodynamic quantities. Bulk boundary correspondence*.

24
Speculations Theory with horizon (AdS, dS, Schwarzschild) A Boundary theory for fluctuations V Area scaling of Fluctuations due to entanglement Statistical ensemble due to restriction of d.o.f V ??? Israel (1976) Maldacena (2001)

25
Fin

Similar presentations

Presentation is loading. Please wait....

OK

Selected Topics in AdS/CFT lecture 1

Selected Topics in AdS/CFT lecture 1

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on electric meter testing Ppt on formal non-formal and informal education Ppt on metallic and non metallic minerals Limbic system anatomy and physiology ppt on cells Ppt on content addressable memory applications Ppt on biodegradable and nonbiodegradable waste Ppt on power diode ppt Ppt on herbs and spices Training ppt on leadership Ppt on bakery business plan