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

We study the entanglement entropy associated with a holographic RG flow from AdS₇ to AdS₄ × ℍ₃, where ℍ₃ 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.