Domain walls for two-dimensional renormalization group flows

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.