Discontinuity in RG Flows Across Dimensions: Entanglement, Anomaly Coefficients and Geometry

We study the entanglement entropy associated with a holographic RG flow from ${\text{AdS}}_7$ to ${\text{AdS}}_4\times {\mathbb{H}}_3$, where ${\mathbb{H}}_3$ is a $3$-dimensional hyperbolic manifold with curvature $\kappa$. 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, $\kappa$. 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.