Discontinuity in RG flows across dimensions: entanglement, anomaly coefficients and geometry

A bstract We study the entanglement entropy associated with a holographic RG flow from AdS 7 to AdS 4 × ℍ 3 , where ℍ 3 is a 3-dimensional hyperbolic manifold with curvature κ . The dual six-dimensional RG flow is disconnected from Lorentz-invariant flows. In this context we address various notions of central charges and identify a monotonic candidate c -function that captures IR aspects of the flow. The UV behavior of the holographic entanglement entropy and, in particular its universal term, display an interesting dependence on the curvature, κ . We then contrast our holographic results with existing field theory computations in six dimensions and find a series of new corrections in curvature to the universal term in the entanglement entropy.