It is commonly believed that exact infra-red (IR) solutions for renormalization group (RG) flows are rare to come by. In this talk, we will consider codimension-one RG flows from pinning fields coupled to bulk local operators in conformal field theories. Using tools from functional analysis, symmetry and anomaly matching, we find exact fixed point solutions for a vast zoo of such flows in d=2,3 and chart the landscape of conformal defects in familiar CFTs.
