We introduce generalized pinning fields in conformal field theory that model a large class of critical impurities at large distance, enriching the familiar universality classes. We provide a rigorous definition of such defects as certain unbounded operators on the Hilbert space and prove that when inserted on codimension-one surfaces they factorize the spacetime into two halves. The possible factorization channels are further constrained by symmetries in the bulk. As a corollary, we solve such critical impurities in the 2d tricritical Ising model and establish the factorization phenomena previously observed for localized mass deformations in the 3d O(N) model. If time permits, I will also explore the characteristics of these defects, including their density of states and the asymptotic behavior of one-point functions.
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Giovanni Rizi, Julio Parra-Martinez
