This document is the syllabus for the PHY 396T Advanced Supersymmetry
course as taught in Spring 2006 by
**
Dr. Vadim Kaplunovsky**;
unique number 59535.
This is a special topics course, it isn't offered every year or every other
year, and the content varies each time.
In particular, this year's course is more advanced than those taught in
2000/01 or 1994/5.

The Advanced Supersymmetry course is aimed at students who have already taken two semesters of Quantum Field Theory, and then spent at least half a semester studying «Basic Supersymmetry» by themselves. Effectively, the Advanced SUSY class is QFT 3½.

Solid knowledge of QFT is essential for understanding SUSY.
However it's your knowledge that matters and not how or where you've acquired it.
Hence, there are no *formal* prerequisites to the SUSY class,
but you must *know* QFT.

Basic SUSY at the Wess & Bagger level (without supergravity) is a perfect
subject for independent study from a textbook.
It's wasteful to spend class time on this material instead of more interesting
advanced subjects.
Thus, I request that *before* the class starts in January 2006,
the students study the following material by themselves:

- SUSY algebra, supermultiplets, and the superspace
(
*N*=1 in*d*=4 only). - Chiral Superfields and their interactions; the superpotential and the Kähler function.
- Abelian vector superfields and SQED; supersymmetric Higgs Mechanism.
- Non-abelian vector superfields.
- Spontaneous supersymmetry breaking.

In terms of textbooks (see below) and their chapters, this material corresponds to:

- Weinberg's volume 3, chapters 25–27.
- Argyres's notes, lectures 1–10.
- Wess & Bagger, chapters 1–11.

All three books cover similar subjects but differ in emphasis and detailedness. I suggest you start with the Argyres's notes and study them in detail, and then browse through Wess & Bagger (or the Superspace book, chapters 2–3) to familiarize yourself with the Weyl-spinor notations I shall use in class. And if you need a more detailed explanation of some subject, look it up in the Weinberg's book, it has everything and more.

I plan to spend most of the class time will be spend on the following subjects:

- Renormalization and no-renormalization theorems.
- Non-perturbative effects in supersymmetric gauge theories.
- Supersymmetric Standard Model and SUSY breaking.

I might say a few words about supergravity, but I will not cover it in any detail.

This course does not follow any particular book, but the following textbooks will be very useful:

- The Quantum Theory of Fields by Steven Weinberg, volume 3. In spite of idiosyncratic notation, this is a very good reference book for almost any subject.
- Philip Argyres's lecture notes for the Supersymmetry course he gave at Cornell are available online at http://www.physics.uc.edu/~argyres/661/.
- Supersymmetry and Supergravity by Julius Wess and John Bagger. A good introduction to basic SUSY. Too low-level for the class itself, but a very good textbook for the self-study pre-requisite.
- Introduction to Supersymmetry by Joseph Lykken, hep-th/9612114. Similar to Wess & Bagger, but shorter and more up-to-date.
- Superspace or 1001 Lesson in Supersymmetry by J.Gates, M.Grisaru, M.Rocek, and W.Siegel. This book is now available on line in PDF format as hep-th/0108200 ( local copy ). Don't print the whole book at UTTG or Physics Dept. printers – it is 585 pages thick.

The homeworks for this course will be assigned in class. Typically, I would ask you to complete (or work out the details of) a calculation began (or sketched out) in class or to read some peripheral-but-interesting material in a textbook or a review article. The homeworks are assigned on the honor system, they will not be graded. Cooperation is encouraged as long as every student thoroughly understands the whole work. (Unlike in the QFT classes I taught before) I will not post solutions on the web, so please check each other's work.

The grade will be based on two take-home exams,
one in the middle of the semester, the other at the end.
Unlike the homeworks, *the exams must be done by
individual students without any help from anybody else!*
There won't be an in-class final exam.

- Mid-term exam is due Tuesday March 28.
- Final exam is due Thursday, May 11.

Note: An equation error was corrected on May 9 at 14:10. Please download the corrected exam.

- Lectures: Tuesdays and Thursdays,
3:30 to 5 PM inRLM 7.112, and Wednesdays2 to 3 PM inRLM 7.114. - Office: RLM-9.314A. Students are welcome whenever I'm in my office and not too busy. The best time to find me is Wednesday after the class, and Thursday after the Brown Bag seminar or after the class.
- Email: vadim@physics.utexas.edu.
Please use e-mail for administrivia or
*simple*questions about homeworks or exams. But if your question needs a long answer, please ask it in person.

- The course will
**continue**through the Fall 2006 semester. - The extension is
*unofficial*, thus no registration or grades. - Lectures
*once*a week, on Mondays from 2 to 3:30 pm, in room RLM 9.202 (same as the brown bag seminar). First lecture on 9/11. - Subjects:
*Supersymmetric Standard Model*and*supersymmetry breaking*.

Last Modified: September 8, 2006. Vadim Kaplunovsky

vadim@physics.utexas.edu