Siegel's lectures, PHY 623, S'20

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.
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.
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.
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).

AdS/CFT

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)