**Fields v4**contains the lecture notes for the class.- ⚠️ This book and web page are being revised
*during*the course. - It may help to have a copy of the relevant subsections available during class (preferably in digital form) for following, annotation, & flipping back to earlier relevant pages.

- ⚠️ This book and web page are being revised
**Assigned reading**is crucial.- It includes @ least 2 subsections ahead of lecture, including the
**homework problems**to be assigned. - Skim the
**background material**to see if you need it. (Some of it is unnecessary, but perhaps interesting elaboration.) - Brief summaries of each subsection are given in the
**Outline**@ the beginning of the book. - Major equations (especially notation & definitions) are collected in the
**AfterMath**@ the end. - If you miss or are late to class, you are responsible for any material you missed: See me in private or ask fellow students.

- It includes @ least 2 subsections ahead of lecture, including the
**Prepare questions**in advance for class.- Find points that were unclear to you in the assigned reading (including background material & homework). The book
*Fields*is my lecture notes, so just listening to me lecture without questions, as a repeat of what you've already read, probably won't be helpful. Lectures aren't YouTube videos. - Prepared annotation of this book is useful for asking questions @ the appropriate points, in case confusion hasn't already been cleared up by then.

- Find points that were unclear to you in the assigned reading (including background material & homework). The book
**Homework**is essential.- It tests whether you understand the lecture.
- If you can't do the homework, you probably won't do well on the exams.
- It's due 1 week after reached in lecture, @ beginning of class, & returned @ the beginning of the following class.
- You can submit it on paper in class, or electronically; if on paper, don't turn in different assignments on the same sheet or you won't get it back till the latest is returned.
- Late homework is not accepted.
**There will be some discussion of the homework in class**, @ the beginning of the lecture when it's returned. More hints will be given for problems students had difficulties with, but not all the algebra will be worked out. You are encouraged to give a second try on problems you failed to complete, for your own edification (not for turning in).

group theory | in subsections | background material & homework |
---|---|---|

conformal group (D>2) | ||

- projective lightcone
- dilatations
- conformal boosts
- inversions
| IA6 | IA6.6-8 (due 3/30) |

coset spaces | IB1 (Hilbert space notation for vector spaces) | |

- global/local
- coordinates/gauges
- covariant derivatives
- representations
- projective
| IC6 | IC6.1 (due 4/1) |

supergroups | IB4-5 (classical groups) | |

- metrics
- grading
| IIC3 | IIC3.2-3 (due 4/10) |

covering groups | IIA4-5 (SL(2) notation) | |

- norms
- Wick rotation
| IC5 | |

CFT₄ | ||

N=4 super Yang-Mills | IVC7 & XC5 (from 4D & 10D superspaces) | |

- indices
- dimensional reduction
| XC6 (1st ¼) | XC6.2 (due 4/13) |

superconformal field theory | IIA7 (chirality/duality) | |

- superconformal groups
- projective superspaces
- 4D N=4 SYM
| IIC4 | IIC4.1 (due 4/13) |

twistors | IIA6 (Dirac spinors), IIB1 (conformal field equations) | |

- coset
- Penrose transform
- helicity
| IIB6-7 | |

supertwistors | ||

- coset
- Penrose transform
- multiplets
| IIC5 | IIC5.1 (due 4/17) |

AdS₅ | ||

(anti) de Sitter space | IXA2 (covariant derivative), IXA7 (Weyl scale) | |

- Einstein's equations
- coordinates
- cosets
- matter field equations
- boundary conditions
| IXC2 | IXC2.3 (due 4/20) |

AdS₅×S⁵ IIB supergravity | IIIC2 (lightcone gauge) | |

- superfield strength
- coset space
- lightcone gauge
- boundary limit
| XC7 | IA2.3 (due 4/24) |

AdS/CFT correspondence | ||

- AdS/CFT conjecture
- couplings
- constraints
- boundary limit
| XIA8 | XIA8.1 (due 4/27) |