  We introduce an effective field theory (EFT) for conformal impurity by
considering a pair of transversely displaced impurities and integrating out
modes with mass inversely proportional to the separation distance. This EFT
captures the universal signature of the impurity seen by a heavy local
operator. We focus on the case of conformal boundaries and derive universal
formulas from this EFT for the boundary structure constants at high energy. We
point out that the more familiar thermal EFT for conformal field theory is a
special case of this EFT with distinguished conformal boundaries. We also
derive, for general conformal impurities, non-positivity and convexity-like
constraints on the Casimir energy which determines the leading EFT coefficient.
