  Surface operators are among the most important observables of the 6d
$\mathcal{N} = (2,0)$ theory. Here we apply the tools of defect CFT to study
local operator insertions into the 1/2-BPS plane. We first relate the 2-point
function of the displacement operator to the expectation value of the bulk
stress tensor and translate this relation into a constraint on the anomaly
coefficients associated with the defect. Secondly, we study the defect operator
expansion of the stress tensor multiplet and identify several new operators of
the defect CFT. Technical results derived along the way include the explicit
supersymmetry tranformations of the stress tensor multiplet and the
classification of unitary representations of the superconformal algebra
preserved by the defect.
