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We study the universal contributions to the entanglement entropy (EE) of 2+1dand 3+1d holographic conformal field theories (CFTs) on topologicallynon-trivial manifolds, focusing on tori. The holographic bulk corresponds toAdS-soliton geometries. We characterize the properties of theseregulator-independent EE terms as a function of both the size of thecylindrical entangling region, and the shape of the torus. In 2+1d, in thesimple limit where the torus becomes a thin 1d ring, the EE reduces to ashape-independent constant $2\gamma$. This is twice the EE obtained bybipartitioning an infinite cylinder into equal halves. We study the RG flow of$\gamma$ 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 theF-theorem. We find that the renormalized $\gamma$ decreases monotonically whenthe holographic CFT is deformed by a relevant operator for all allowed scalingdimensions. We also discuss the question of non-uniqueness of such renormalizedEEs both in 2+1d and 3+1d.

Holographic torus entanglement and its RG flow