Entanglement C-functions of defects and interfaces in $\mathcal{N}=4$ supersymmetric Yang-Mills theory

We consider planar codimension-one defects and interfaces in $\mathcal{N}=4$ supersymmetric Yang-Mills (SYM) theory, realized by the D3/D5-brane intersection. Working in the probe limit, where the number of D5-branes is small compared to the number of D3-branes, we obtain analytic results for the holographic entanglement entropy of a ball-shaped region centered on the defect. A defect renormalization group flow is triggered by giving the defect hypermultiplets a mass, which corresponds to separating the D3- and D5-branes. Along this flow the entanglement C-function decreases monotonically. We also allow the D5-branes to carry worldvolume flux corresponding to dissolved D3-branes, in which case the setup describes an interface between two copies of $\mathcal{N}=4$ SYM theory with different gauge groups, where an RG flow is triggered by a mass term for vector multiplets. Here we again find monotonic behavior of the entanglement C-function, although its interpretation as a measure of effective degrees of freedom is problematic. We investigate possible alternative measures of degrees of freedom.