Interacting conformal scalar in a wedge

We study a class of two-point functions in a conformal field theory near a wedge. This is a set-up with two boundaries intersecting at an angle $\theta$. We compute it as a solution to the Dyson-Schwinger equation of motion for a quartic interaction in the $d=4-\epsilon$ bulk and in the $d=3-\epsilon$ boundary, up to order $\mathcal{O}(\epsilon )$. We have extracted the anomalous dimensions from such correlators and we have complemented them with Feynman diagrams computations.