  We study defect CFT within the framework of holographic duality, emphasizing
the impact of corner contributions. We model distinct conformal defects using
interface branes that differ in tensions and are connected by a corner.
Employing the relationship between CFT scaling dimensions and Euclidean gravity
actions, we outline a general procedure for calculating the anomalous
dimensions of defect changing operators at nontrivial cusps. Several analytical
results are obtained, including the cusp anomalous dimensions at big and small
angles. While $1/\phi$ universal divergence appears for small cusp angles due
to the fusion of two defects, more interestingly, we uncover a bubble phase
rendered by a near zero angle cusp, in which the divergence is absent.
