Epfl Lectures On Conformal Field Theory In D 3 Dimensions

EPFL Lectures on Conformal Field Theory in D >

EPFL Lectures on Conformal Field Theory in D ≥ 3 Dimensions

This primer develops Conformal Field Theory (CFT) from scratch, whereby CFT is viewed as any conformally-invariant theory that describes a fixed point of a renormalization group flow in quantum field theory. The book is divided into four lectures: Lecture 1 addresses the physical foundations of conformal invariance, while Lecture 2 examines the constraints imposed by conformal symmetry on the correlation functions of local operators, presented using the so-called projective null cone – a procedure also known as the embedding formalism. In turn, Lecture 3 focuses on the radial quantization and the operator product expansion, while Lecture 4 offers a very brief introduction to the conformal bootstrap. Derived from course-based notes, these lectures are intended as a first point of entry to this topic for Master and PhD students alike.

Line Defects in Conformal Field Theory

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 Yang–Mills, 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.