Quantum holographic entanglement entropy to all orders in 1/N expansion

Abstract

We study holographic entanglement entropy in four-dimensional quantum gravity with negative cosmological constant. By using the replica trick and evaluating path integrals in the minisuperspace approximation, in conjunction with the Wheeler-DeWitt equation, we compute quantum corrections to the holographic entanglement entropy for a circular entangling surface on the boundary three sphere. Similarly to our previous work on the sphere partition function, the path integrals are dominated by a replica version of asymptotically AdS conic geometries at saddle points. As expected from a general CFT argument, the final result is minus the free energy on the three sphere which agrees with the logarithm of the Airy partition function for the ABJM theory that sums up all perturbative 1/N corrections despite the absence of supersymmetries. The all-order holographic entanglement entropy cleanly splits into two parts, (1) the 1/N -corrected Ryu-Takayanagi minimal surface area and (2) the bulk entanglement entropy across the minimal surface, as suggested in the earlier literature. It is explicitly shown that the former comes from the localized conical singularity of the replica geometries and the latter from the replication of the bulk volume. † shinji.hirano@wits.ac.za

Carl Sagan

“…We studied in section 7.4.3 the input is actually lost with such simplification. We have already mentioned how the ABJM superconformal field theory three-sphere partition function can be recovered exactly with a minisuperspace path integral [150,152]. It is an interesting question to ask whether this is just a fortunate coincidence or the minisuperspace approximation does indeed already include all of the relevant information in specific physical situations.…”

“…We work 23 See also Ref. [152] for another recent application of the minisuperspace approach in holography.…”