Introduction to conformal field theory

This course offers an introduction to conformal field theory (CFT) in dimensions higher than two.

 

We start by exploring continuous phase transitions in statistical physics, using the Ising model in d dimensions as a prototypical example. We'll discuss how the renormalization group (RG) flow leads to scale (and conformal) invariance at large distances and demonstrate how critical exponents are related to the scaling dimensions of operators.

 

Next, we explore the foundations of CFTs. We begin by analyzing conformal symmetry, examining both finite and infinitesimal transformations, the algebra, and how it can be generated from the stress tensor. We'll explore how this symmetry constrains the kinematics of correlation functions. Moving on, we cover the quantization of the theory and show how radial quantization provides a correspondence between states and operators. We also discuss unitarity/reflection positivity and cover the operator product expansion (OPE). The course concludes with an explanation of how, by combining the concepts introduced, one can compute the critical exponents of a CFT —such as the 3d Ising model— using the conformal bootstrap.