Holographic entanglement entropy of surface defects

We calculate the holographic entanglement entropy in type iib supergravity solutions that are dual to half-bps disorder-type surface defects in $$ mathcal{n}=4 $$ supersymmetric yang-mills theory. the entanglement entropy is calculated for a ball-shaped region bisected by a surface defect. using the bubbling supergravity solutions we also compute the expectation value of the defect operator. combining our result with the previously-calculated one-point function of the stress tensor in the presence of the defect, we adapt the calculation of lewkowycz and maldacena [1] to obtain a second expression for the entanglement entropy. our two expressions agree up to an additional term, whose possible origin and significance is discussed.