On co-dimension two defect operators

Abstract: Conformal symmetry is broken by a flat or spherical defect operator $\mathcal{D}$. We show that this defect operator, may be identified as a pair of twist operators which are inserted at the tips of its causal diamond. Any $k-$point correlation function in a flat or spherical defect CFT is equivalent to a $(k+2)-$point correlation function. We reproduce one point correlation functions and also solve two point correlation functions in defect CFTs . Mutual R\'enyi entropy is computed and agrees with previous result in a certain limit. We conjecture there may be universal terms in general co-dimension two defect CFTs.