Quantum corrections to finite radius holography and holographic entanglement entropy

William Donnelly, Elise LePage, Yan-Yan Li, Andre Pereira, Vasudev Shyam
2020 Journal of High Energy Physics  
We calculate quantum corrections to holographic entanglement entropy in the proposed duality between TT -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
more » ... urface 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.
doi:10.1007/jhep05(2020)006 fatcat:7ifzetfkkvhc3k5o7xggo7tjae