2019/09/30 by William Donnelly, Elise LePage, Yan-Yan Li +2 · 21 citations
Physics and Astronomy · #Antipodal point #Black Holes and Theoretical Physics #Conformal field theory #Entropy (arrow of time) #Holography #Joint quantum entropy #Noncommutative and Quantum Gravity Theories #Path integral formulation #Quantum entanglement #Quantum many-body systems #Quantum relative entropy #Squashed entanglement #gr-qc #hep-th
paper · pdf · doi:10.1007/jhep05(2020)006
published in Journal of High Energy Physics 2020(5) (Springer Nature) · 25 pages, 1 figure. references updated in v2
openalex created_date 2019/10/03 · arxiv created 2019/12/20 · openalex publication_date 2020/05/01 · arxiv updated 2020/05/20 · openalex updated_date 2026/08/05
A bstract We calculate quantum corrections to holographic entanglement entropy in the proposed duality between TT <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> <mml:mover> <mml:mi>T</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> -deformed holographic 2D CFTs and gravity in AdS 3 with a finite cutoff. We first establish the dictionary between the two theories by mapping the flow equation of the deformed CFT to the bulk Wheeler-DeWitt equation. The latter reduces to an ordinary differential equation for the sphere partition function, which we solve to find the entanglement entropy for an entangling surface consisting of two antipodal points on a sphere. The entanglement entropy in the inverse central charge expansion yields the expectation value of the bulk length operator plus the entropy of length fluctuations, in accordance with the Ryu-Takayanagi formula and its generalization due to Faulkner, Lewkowycz, and Maldacena. Special attention is paid to the conformal mode problem and its resolution by a choice of contour for the gravitational path integral.