Abstract

Nonlocal conformal field theory is the proper language for studying critical phenomena in systems with all-to-all interactions between spins. It is also arises inevitably in defects which belong to local CFTs in a higher dimensional space. Both of these concepts are exemplified by the long-range Ising model which can be viewed as an interacting defect for a free field in two different ways. One description is weakly coupled when the other is strongly coupled, providing an instance of infrared duality. This talk will focus on efforts to establish a similar understanding for long-range versions of so called m-th minimal models where Ising is the case of m = 3. For one family, a similar duality is known. For other families, finding one (or proving that it does not exist) is an open problem. I will discuss a possible hint in the form of a stark difference between these families which arises at large m. Along the way, we will also encounter some underappreciated technology for conformal perturbation theory.