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Conformal symmetry is broken by a flat or spherical defect operator$\mathcal{D}$. We show that this defect operator, may be identified as a pairof 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 equivalentto a $(k+2)-$point correlation function. We reproduce one point correlationfunctions and also solve two point correlation functions in defect CFTs .Mutual R\'enyi entropy is computed and agrees with previous result in a certainlimit. We conjecture there may be universal terms in general co-dimension twodefect CFTs.

On co-dimension two defect operators