Course curriculum

  • 1

    Outline

    • Course Outline

    • CFT notes

    • Anomalies notes

    • String theory notes

    • Perusall
  • 2

    CFT - Week 1

    • Week 1 Guide

    • CFT notes

    • Additional references

    • Introduction to conformal field theory

    • Conformal transformations

    • Why CFT? - Asymptotic low energy QFT

    • Why CFT? - Massive QFTs as deformations

    • Dimensional analysis

    • Why CFT? - Ordering in space of QFTs

    • Why CFT? - Phase transitions

    • Why CFT? - Quantum gravity

    • Why CFT? - String theory

    • Lecture 1 blackboard screenshots

    • Introduction

    • Kinematics introduction

    • Conformal transformations

    • Conformal algebra introduction

    • Conformal Killing vectors

    • Conformal algebra from Lie bracket

    • AdS/CFT symmetries

    • Discrete conformal transformations

    • Lecture 2 blackboard screenshots

    • Geometry of conformal symmetry

    • Stress-energy tensor

    • Local operators

    • Transformations of primary operators

    • Lecture 3 blackboard screenshots

    • Tutorial 1: Energy-momentum tensor

    • Solution 1

    • Comments or questions?
  • 3

    CFT - Week 2

    • Week 2 Guide

    • Position dependence of correlation functions

    • Quiz 2: One-point function

    • Two and three point functions

    • $$N\geq 4 $$ point functions

    • Cross ratios

    • 4 point function

    • Operator product expansion (OPE) introduction

    • OPE for 3-point function

    • OPE for 4-point function

    • Radius of convergence and consistency conditions

    • Lecture 4 blackboard screenshots

    • Conformal bootstrap

    • Anomalies introduction

    • Conformal anomaly in D=2

    • Geometric view of anomalies

    • Lecture 5 blackboard screenshots

    • Tutorial 2: Correlation functions

    • Solution 2

    • Homework 1: Conformal invariance of Maxwell action and axial anomaly

    • Comments or questions?
  • 4

    Anomalies - Week 3

    • Week 3 Guide

    • Anomalies notes - several small corrections on March 17 (Thanks Shuwei!)

    • Introduction to anomalies

    • Chiral anomaly in 2D massless QED introduction

    • Classical massless QED

    • Quantizing the fermion

    • Functional integral derivation of chiral anomaly introduction

    • Functional integral measure and the chiral anomaly

    • Regularization and the anomaly

    • Tutorial 3: Chiral anomaly

    • Solution 3

    • Comments or questions?
  • 5

    String Theory - Week 4

    • String theory notes

    • Week 4 guide

    • String perturbation theory

    • String tension and energy scales

    • Uniqueness of string theory

    • D-branes and open strings

    • Dualities

    • D-branes and open strings

    • Lecture 1 blackboard screenshots

    • Nambu-Goto and Polyakov actions

    • Feynman diagrams as worldline integrals

    • Gauge fixing and complex structure

    • Space of complex structures

    • Weyl anomaly

    • Lecture 2 blackboard screenshots

    • Mode expansion and Fock space

    • Symmetries

    • Stress tensor

    • Stress Tensor

    • Virasoro algebra

    • Lecture 3 blackboard screenshots

    • Tutorial 4: Classical string

    • Solution 4

    • Homework 2: String spectrum and Virasoro algebra

    • Comments or questions?
  • 6

    String Theory - Week 5

    • Week 5 Guide

    • Physical and null states

    • String spectrum

    • Lecture 4 blackboard screenshots

    • Compactification and T-duality

    • Lecture 10 blackboard screenshots

    • QED coupled to a proton

    • D-branes and strings

    • State space

    • Boundary conditions

    • Boundary conditions

    • Lecture 11 blackboard screenshots

    • Boundary conditions in CFT

    • Chan-Paton bundles

    • Boundary local operators

    • Boundary conditions for scalar fields

    • D-branes as string sources

    • Open string spectrum

    • Lecture 12 screenshots

    • Tutorial 5: T-duality and D-branes

    • Solution 5

    • Additional videos

    • Bonus Q&A with Davide: Thursday 8 April at 4pm Waterloo time

    • Comments or questions?