Week 20.04.2026 – 26.04.2026

Our understanding of interacting CFTs in d>2 dimensions was revolutionized by modern developments in the analytical and numerical conformal bootstrap. The poster child of this program, the non-exactly solvable 3d Ising CFT, is now understood to an unprecedented level of detail. In contrast, our understanding of 2d CFTs encompasses large classes of exactly solvable models (the so-called rational CFTs), and a set of universal bootstrap results which apply only to "generic" non-exactly solvable CFTs of which no concrete example is available. In this talk, we summarize our recent attempts at constructing such theories by coupling exactly solvable CFTs and flowing to IR fixed points. We will discuss perturbative and non-perturbative constructions as well as some dual bounds on the set of conserved currents in the IR.