This book investigates conformal line defects in both the weak- and strong-coupling regimes. Conformal field theory finds applications across diverse fields, from statistical systems at criticality to quantum gravity through the AdS/CFT correspondence. These theories are subject to strong constraints, enabling a systematic non-perturbative analysis. Conformal defects provide a controlled means of breaking the symmetry, introducing new physical phenomena while preserving crucial benefits of the underlying conformal symmetry. Two distinct classes of models are studied. First, we focus on the supersymmetric Wilson line in N = 4 Super YangMills, which serves as an ideal testing ground for the development of innovative techniques such as the analytic conformal bootstrap. The second class consists of magnetic lines in Yukawa models, which have fascinating applications in 3d condensed-matter systems. These systems have the potential to emulate phenomena observed in the Standard Model in a low-energy setting.
Chapter
1. INTRODUCTION.
Chapter
2. FOUNDATIONS.
Chapter
3. BOOTSTRAPPING HOLOGRAPHIC DEFECT CORRELATORS.
Chapter
4. MULTIPOINT CORRELATORS ON THE WILSON-LINE DEFECT CFT.
Chapter
5. LINE DEFECT CORRELATORS IN FERMIONIC CFT.
Chapter
6. CONCLUSIONS.
Julien Barrat, born in Nancy (France), is a physicist specializing in theoretical physics. He obtained his Bachelor's degree in Physics from Humboldt University, Berlin (Germany), with a thesis focusing on nanostructure fabrication under the guidance of Prof. Catherine Dubourdieu. His passion for theoretical physics led to a Master's thesis on quantum field theory, with a focus on Wilson lines in the N=4 Super Yang-Mills theory, supervised by Prof. Dr. Jan Plefka and Dr. Thomas Klose. Julien then pursued a PhD within the "RTG 2575: Rethinking Quantum Field Theory" training group, under the mentorship of Jan Plefka and Valentina Forini from 2020 to 2023. During this time, he actively engaged in outreach through the "Non-Standard Models" project, contributing to educational YouTube videos on theoretical physics. Since October 2023, Julien is a postdoctoral researcher at DESY, Hamburg (Germany), working in the group of Prof. Elli Pomoni.
