Holographic entanglement entropy from probe M-theory branes

We compute the holographic entanglement entropy contribution from planar two-dimensional defects in six-dimensional $\mathcal{N}=(2,0)$ superconformal field theory, holographically dual to probe M2- and M5-branes in $AdS_7 \times S^4$. In particular, we test the viability of the universal contribution of the defect to entanglement entropy as a candidate $C$-function. We find that this coefficient is not monotonic under defect renormalization group flows triggered by the vacuum expectation value of a marginal operator. Another candidate $C$-function, the on-shell action inside the entanglement wedge, monotonically decreases under the flows we study.