Holographic torus entanglement and its renormalization group flow

We study the universal contributions to the entanglement entropy (EE) of 2 + 1-dimensional and 3 + 1-dimensional holographic conformal field theories (CFTs) on topologically nontrivial manifolds, focusing on tori. The holographic bulk corresponds to anti-de Sitter-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 + 1 dimensions, in the simple limit where the torus becomes a thin one-dimensional ring, the EE reduces to a shape-independent constant 2 gamma. This is twice the EE obtained by bipartitioning an infinite cylinder into equal halves. We study the renormalization group flow of. 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. 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 nonuniqueness of such renormalized EEs both in 2 + 1 dimensions and 3 + 1 dimensions.