Holographic torus entanglement and its renormalization group flow

Abstract

We study the universal contributions to the entanglement entropy (EE) of 2+1d and 3+1d holographic conformal field theories (CFTs) on topologically non-trivial manifolds, focusing on tori. The holographic bulk corresponds to AdS-soliton geometries. We characterize the properties of these regulator-independent EE terms as a function of both the size of the cylindrical entangling region, and the shape of the torus. In 2+1d, in the simple limit where the torus becomes a thin 1d ring, the EE reduces to a shape-independent constant 2γ. This is twice the EE obtained by bipartitioning an infinite cylinder into equal halves. We study the RG flow of γ by defining a renormalized EE that 1) is applicable to general QFTs, 2) resolves the failure of the area law subtraction, and 3) is inspired by the F-theorem. We find that the renormalized γ decreases monotonically at small coupling when the holographic CFT is deformed by a relevant operator for all allowed scaling dimensions. We also discuss the question of non-uniqueness of such renormalized EEs both in 2+1d and 3+1d.

Entanglement entropy in generalised quantum Lifshitz models

“…where κ d is a numerical coefficient that depends on the number of dimensions d. Similar behaviour was obtained for the three-dimensional torus in conformal field theories in [65] (see also [66]), and also in [67] from a holographic approach.…”

Entanglement entropy of singular surfaces under relevant deformations in holography

“…where there are infinitely many linear combinations of these operators with different n that reproduce the same F U V while they give different flows away the CF T fixed point. This ambiguity in introducing the renormalization operator was reported earlier in [47,48]. To choose the correct operator, one needs to apply some extra physical conditions.…”

“…In addition, there is a 1/δ singularity in the Gauss-Bonnet gravity. 48) in this case, there is a logarithmic term both in the Einstein and the Gauss-Bonnet gravities. The 1/δ singularity emerges in the Gauss-Bonnet case.…”

Non-local observables at finite temperature in AdS/CFT

“…is conserved. 19 Consequently, the embedding for an extremal surface with turning point z is described by…”

“…and prove its monotonicity using the null energy condition. An example of this involving a torus was studied in [19]. For a conformal field theory in even dimensions, c d is related to the central charge given by the topological contribution to the conformal anomaly [1,20,21].…”