A defective approach to the conformal bootstrap

Abstract

Defects are an inherent part of statistical and condensed matter systems in the real world. At criticality, the problem of describing the interplay of defect and bulk degrees of freedom requires the application of state-of-the-art techniques in quantum field theory. When the bulk is described by a conformal field theory, the problem becomes especially rich due to thestructure of consistency conditions following from conformal invariance. In this thesis, we develop a new set of numerical conformal bootstrap tools to constrain aspects of CFTs in the presence of defects of various kinds, and in various spacetime dimensions. We first devise a general technique for studying the consequences of ‘t Hooft anomalies in two dimensional conformal field theories, which we use to quantify the general result that anomalies guarantee low-energy, charged degrees of freedom. The approach combines the constraints of modular invariance and crossing symmetry of symmetry defect operators. We then demonstrate a new way to study endable line defects in CFTs in any dimension in a way that rigorously incorporates aspects of the bulk CFT data. We study the particular case of the pinning field defect of the 3d Ising CFT, deriving rigorous bounds on a number of quantities that characterize it.