A Modern Study of Extended Objects in Conformal Field Theory

Abstract

Conformal Field Theories (CFTs) are ubiquitous in modern theoretical physics and play an important role in high-energy physics and condensed matter physics alike, describing the universal behavior of second-order phase transitions. The notion of a CFT can be generalized by introducing extended objects, or defects. These defects, breaking part of the conformal symmetry, give access to new observables, and provide interesting new dynamics. Conformal defects are those that preserve conformal symmetry on the defect, and can be studied with similar methods employed to study CFTs without extended objects. In particular, one can use well-known perturbative methods such as the ε-expansion to compute critical exponents, or employ a modern approach and use the conformal bootstrap to constrain bulk and defect CFT data. In this thesis we study a plethora of conformal defects, ranging from highly constraining supersymmetric setups to physical and experimentally realizable setups without supersymmetry, including interactions between scalars and fermions. We will use the ε−expansion and the conformal bootstrap, and in this way combine the old and the new.