Aspects of Defects in Conformal Field Theory

Abstract

In this thesis, we study the properties of several types of conformal defects, which are extended operators in conformal field theory that preserve a subgroup of the conformal group SO(p + q + 1, 1) -> SO(q) × SO(p + 1, 1). In the presence of a defect, new conformal data emerges due to local excitations on the defect. We focus on analytic methods of extracting this data and, where applicable, discuss checks of proposed monotonic quantities in RG flows. Chapter 2 is based on work with Simone Giombi and Himanshu Khanchandani. We study RG interfaces, which are codimension 1 defects defined by turning on a relevant deformation on half space and tuning to an IR fixed point on half space. We focus on deformations created by double-trace operators of large N CFTs. After setting up the large N expansion using a Hubbard-Stratonovich transformation on half space, we compute some defect CFT data and calculate the free energy when the theory is placed on a sphere. We then discuss the holographic description of the model and show manifest equivalence between the AdS and CFT calculations of one-, two-, and three-point functions. Chapter 3 is based on work with Simone Giombi and Himanshu Khanchandani. We study line defects in fermionic CFTs and show the existence of a nontrivial stable IR fixed point at the endpoint of an RG flow localized on a line defect in the Gross- Neveu-Yukawa universality class. Keeping the bulk at a perturbative Wilson-Fisher fixed point at d = 4 − ε, we compute the beta function of the defect coupling and extract a variety of defect CFT data. Chapter 4 is based on work with Simone Giombi, Ziming Ji, and Himanshu Khanchandani. We study a codimension 2 monodromy defect in the O(N) model in d dimensions. We find the problem is convenient to map to R^d -> H^(d-1) x S^1 and compute data in the free and interacting O(N) model. We then provide some checks of the conjectured “defect C-theorem” by comparing the logarithm of the expectation value of the defect before and after defect RG flows.