This document is the syllabus for the PHY 396T Advanced Supersymmetry
course as taught in Fall 2013 by
**
Dr. Vadim Kaplunovsky**.
This is a special topics course, it isn't offered every year or every other
year, and the content varies each time.

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

This class is about supersymmetric quantum field theories, and I presume the
students already know QFT at the 2-semester level; if you do not know QFT
you would not be able to follow this class.
I do not raise any *formal* prerequisites because it's the knowledge that
matters and not how or where you have acquired it.

If you are not sure of your knowledge, please take a look at the exams for the QFT classes I taught in 2012/13: QFT I midterm, QFT I final, QFT II midterm, QFT II final. If you can do all the exams, you are ready for SUSY, but if you don't know how to solve some of the problems, then you must beef up your QFT before taking the SUSY class.

Basic SUSY at the Wess & Bagger level (without supergravity) is a perfect
subject for independent study from a textbook, and it would be
wasteful to spend class time on this material instead of more interesting
advanced subjects.
Thus, I request that *before* the class starts on 8/29/2013,
the students study the following material by themselves:

- SUSY algebra, supermultiplets, the
*N*=1 superspace in*d*=4, and the spinor derivatives D_{α}and D̅_{α̇}. - Chiral Superfields and their interactions; the superpotential and the Kähler function.
- Abelian vector superfields and the SQED.
- Non-abelian vector superfields.
- Higgs mechanism in SUSY gauge theories.
- Spontaneous supersymmetry breaking.

In terms of the textbooks 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.

The class will focus on the following subjects:

- Renormalization and no-renormalization theorems.
- Non-perturbative effects in supersymmetric gauge theories.
- Supersymmetric dualities.
- The Supersymmetric Standard Model.
- How to break SUSY and how to tell the SSM that it's broken.

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. Despite its idiosyncratic notations, 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.
- Cambridge Lectures on Supersymmetry and Extra Dimensions by Sven Krippendorf, Fernando Quevedo, Oliver Schlotterer, arXiv:1011.1491. 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 at arXiv:hep-th/0108200. Please don't print the whole book at UTTG or Physics Dept. printers — it is 585 pages thick.
- Modern Supersymmetry: Dynamics and Duality by John Terning. Covers the advanced subjects I will discuss in class. The UT library has this book in electronic form.

I shall follow the same system I used in my QFT classes I taught last year. The homeworks will be assigned on the honor system: I shall not collect or grade them, but you should endeavor to finish them on time and check each other's solutions.

The homeworks will be posted on this web page. I shall try to post them more-or-less weekly, but the schedule would not be as regular as in the QFT classes. Also, I shall not post all the solutions, although I might post a few.

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.

- Lectures: 4 hours a week:
- Tuesdays and Thursdays, 3:30 to 5:30, room RLM 5.116.
- Note: Each lecture is 2 hours rather than an hour and a half.
- For your convenience, I keep a log of lectures I gave thus far, and what I plan to say in the next lecture or two.

- Office: RLM-9.314A. Students are welcome whenever I'm in my office and not too busy.
- 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.

This class will contunue through the Spring 2014 semester. The extension is un-official, so there would be no registration or grades, but all the students who took the class in the Fall 2013 are welcome to participate.

Since different students have asked for lectures on different subjects, I shall try to cover several issues. Before the spring break, I shall focus on the more formal subjects: N=2 SUSY, SUSY in higher dimensions, and introduction to supergravity. After the break, I shall turn to the MSSM and its phenomenology, the spontaneous breakdown of SUSY, and the mediation of this breakdown to the MSSM.

In the Spring, we shall meet on Fridays from 1 to 2:30 or 3 PM, in the brown bag room RLM 9.222.

Last Modified: January 14, 2014. Vadim Kaplunovsky

vadim@physics.utexas.edu