  Renormalization Group domain walls are natural conformal interfaces between
two CFTs related by an RG flow. The RG domain wall gives an exact relation
between the operators in the UV and IR CFTs. We propose an explicit algebraic
construction of the RG domain wall between consecutive Virasoro minimal models
in two dimensions. Our proposal passes a stringent test: it reproduces in
detail the leading order mixing of UV operators computed in the conformal
perturbation theory literature. The algebraic construction can be applied to a
variety of known RG flows in two dimensions.
