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On the role of gravity in Holography

On the role of gravity in Holography. Current work: A Minkowski observer restricted to part of space will observe: Radiation. Area scaling of thermodynamic quantities Bulk boundary correspondence*. Future directions: Kruskal observer AdS observer Entanglement of a single string

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On the role of gravity in Holography

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  1. On the role of gravity in Holography • Current work: A Minkowski observer restricted to part of space will observe: • Radiation. • Area scaling of thermodynamic quantities • Bulk boundary correspondence*. • Future directions: • Kruskal observer • AdS observer • Entanglement of a single string • Experimental verification

  2. out out in in V V A Minkowski observer in part of Minkowski space. No access Restricted measurements =

  3. Trout(y’ y’’ rin(y’in,y’’in) =   Exp[-SE] DfDout 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) in y’in y’’in Exp[-SE] Df f(x,0+) = y’in(x)yout(x) y’in(x) y’(x) y’’(x) f(x,0-) = y’’in(x)yout(x) x y’’in(x) f(x,0+) = y’in(x) f(x,0-) = y’’in(x) Radiation

  4. in y’in y’’in Exp[-SE] Df f(x,0+) = y’in(x) f(x,0-) = y’’in(x) t y’in(x) x y’’in(x) Explicit example Kabbat & Strassler (1994)  ’| e-bHR|’’

  5. out in V Thermodynamics

  6. Entropy: Sin=Tr(rinlnrin) Srednicki (1993) Sin=Sout

  7. Other quantities R. Brustein and A.Y. (2003) Heat capacity: Generally, we consider:

  8. F(x)=2f(x) Since F(x) =  eiqxcosqF(q) ddq D(x)=V V d(xxy) ddx ddy and F (q) ~ qa = GVVxd-1 – GSS(V)xd+O(xd+1)  ∂ x(D(x)/xd-1)   S Area scaling of fluctuations (OV)2 = V V O(x)O(y) ddx ddy =V V F(|x-y|) ddx ddy = D(x) F(x) dx  (OV)2  = - ∂ x(D(x)/xd-1)xd-1 ∂xf(x) dx Introduce U.V. cutoff short~ 1/L distances

  9. V2 OV1OV2 V1 OV1OV2  S(B(V1)B(V2)) OV1OV2 Evidence for bulk-boundary correspondence OV1OV2- OV1OV2  V1 V2 Pos. of V2 Pos. of V2

  10. A working example Large N limit

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

  12. Future directions • Kruskal observer • AdS observer • Entanglement of a single string • Experimental verification

  13. V V V Kruskal observer Restricted observer Kruskal Observer Schwarschield observer General relation Israel (1976) Non unitary evolution of rin

  14. AdS ? AdS ? V V V AdS observer CFT ?

  15. Experimental verification • Prepare a pure quantum state. • Make repetitive measurements. • Measure part of the system.

  16. l Entanglement of a single string (DM)2ln(l)

  17. Summary • Radiation, area scaling laws and a bulk-boundary correspondence may be attributed to entanglement. • It is unclear whether gravity alone is responsible for area dependent quantities or if it is supplemented by quantum entanglement.

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