Young Researchers School 2024 Maynooth: Lectures on CFT, BCFT and DCFT

TL;DR

This paper provides an educational overview of Conformal Field Theory, Boundary CFT, and Defect CFT, covering foundational concepts, boundary and defect operators, and the construction of Verlinde lines, aimed at young researchers.

Contribution

It offers a self-contained set of lecture notes introducing core concepts and formalism of CFT, BCFT, and DCFT with exercises and solutions for early-career researchers.

Findings

Introduction to conformal families and fusion rules

Formalism for boundary and defect state spaces

Construction and analysis of Verlinde lines

Abstract

These notes were presented at the Young Researchers School (YRS) in Maynooth in April 2024 and provide an introduction to Conformal Field Theory CFT, Boundary Conformal Field Theory (BCFT) and Defect Conformal Field Theory (DCFT). This class is mostly self-contained and includes exercises with solutions. The first part of these notes is concerned with the basics of CFT, and was taught by the author during the pre-school for the YRS 2024. Here the aim is to convey the notion of conformal families, their fusion and the construction of partition functions. The second part of these notes is dedicated to boundaries and defects in CFT and was presented by the author at the main school. As far as boundaries are concerned, emphasis is placed on boundary operators and their state spaces, as well as the boundary state formalism with the Cardy constraint. Topological defects are discussed in analogy, i.e. defect state spaces and the relevant consistency constraint are derived. Verlinde lines are constructed as their simplest solution and their properties are inspected.