TASI Lectures on the Conformal Bootstrap

TL;DR

This paper provides an educational overview of conformal field theory fundamentals, including key principles, mathematical tools, and an introduction to numerical bootstrap methods applied to 2D and 3D Ising models.

Contribution

It offers a comprehensive pedagogical introduction to conformal bootstrap techniques and their application to critical phenomena in statistical models.

Findings

Explanation of conformal Ward identities and operator product expansion

Introduction to numerical bootstrap methods for Ising models

Foundational concepts for conformal field theory analysis

Abstract

These notes are from courses given at TASI and the Advanced Strings School in summer 2015. Starting from principles of quantum field theory and the assumption of a traceless stress tensor, we develop the basics of conformal field theory, including conformal Ward identities, radial quantization, reflection positivity, the operator product expansion, and conformal blocks. We end with an introduction to numerical bootstrap methods, focusing on the 2d and 3d Ising models.