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SUMMARY:Holographic entanglement and quantum gravity in finite regions - W
 illiam Donnelly (Perimeter)
DTSTART:20191024T120000Z
DTEND:20191024T130000Z
UID:TALK131104@talks.cam.ac.uk
CONTACT:Dr. Carl Turner
DESCRIPTION:The TT̄ deformation of two-dimensional holographic conformal 
 field theory is conjectured to be dual to quantum gravity in a finite regi
 on of three-dimensional anti-de Sitter spacetime. We study entanglement en
 tropy in this theory and its relation to quantum fluctuations of the dual 
 geometry. We derive the correspondence between the TT̄ flow equation and 
 the Wheeler-DeWitt equation with a negative cosmological constant. By fixi
 ng the resulting emergent diffeomorphism symmetry\, we obtain a differenti
 al equation for the sphere partition function which can be solved exactly.
  The solution can be expressed as a Euclidean path integral along a partic
 ular complex contour. We then apply this result to study entanglement entr
 opy of the boundary theory for an entangling surface consisting of two ant
 ipodal points on the sphere. The entanglement entropy gives the Ryu-Takaya
 nagi formula for a geodesic in a finite region plus quantum corrections. W
 e suggest an interpretation of the latter as entropy of fluctuations of th
 e bulk geodesic length\, in accordance with the proposal of Faulkner\, Lew
 kowycz\, and Maldacena.\n\nBased on arXiv:1909.11402 with E. LePage\, Y. L
 i\, A. Pereira and V. Shyam.
LOCATION:Potter Room (first floor\, Pav. B)
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