This document is the syllabus for the PHY 396T Advanced Supersymmetry course as taught in Fall 2025 by Dr. Vadim Kaplunovsky (unique number TBA). This is a special topics course, it isn't offered every year or every other year, and the content varies each time.
This course does not follow any particular book, but the following textbooks will be very useful:
Besides the textbooks, I wrote a few supplementary notes for the class, and I expect to write a few more. All these notes are linked to this page.
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 2024/25: QFT I midterm, QFT I final, QFT II midterm, QFT II final. If you can do all the exams, you are ready for the SUSY class. But if you have no idea how to solve some of the problems, you should take the QFT I and QFT II classes first.
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 8/26/2025, the students study the following material by themselves:
In terms of the textbooks and their chapters, the first 4 subjects correspond to:
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.
As to the last subject – the superspace Feynman rules, – the best reference is the Superspace book, sections 6.1–4.
Supersymmetry is a rather wide field involving many subjects. But this class will primarily focus on the N=1 exactly supersymmetric theories in 4 dimensions, especially on the:
On the other hand, the class will not cover the supersymmetric standard model, the supergravity, or the spontaneous supersymmetry breaking. As interesting as these subjects may be, I simply cannot squize them into a 1-semester class.
The homeworks are absolutely essential for understanding the course material. Often, due to the time pressure, I will explain the general theory in class and leave the examples for the homework assignment. It is extremely important for you to work them out by yourselves; otherwise, you might think you understand the class material but you would not! Be warned: The homeworks will be very hard.
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. And once the homework is due, I shall post the solutions.
Similarly to my QFT classes, there will be no in-class final exam for the SUSY class. Instead, grades will be based 50/50 on two week-long take-home exams: The midterm exam in late October, and the final exam in December.
I shall use Canvas to schedule Zoom sessions for all the lectures; this way, the lectures would be recorded and you would find the records on Canvas. Apart from that (and the mandatory posting of this syllabus to Canvas), I shall not use Canvas for anything else. In particular, all homeworks and exams will be posted to the homework page rather than to Canvas, and the exam grades shall be emailed directly to the students.
Similar to the QFT classes, the SUSY class will be rather intense. In particular, we shall have four hours of regular lectures every week, and a lot of hard homework.
Assuming UT continues to provide technical support, all lectures should be mirrored online via Zoom and their recording available to the students via Canvas. However, I strongly urge all students to come to the lectures in person if they can, or at least to watch them in real time via Zoom.
I do not plan to give any extra lectures for the SUSY class. However, if a regular lecture would be canceled for any reason, I shall schedule a replacement lecture to make up for it, Also, if I see that some students don't have the background knowledge they need to follow the class material, I shall schedule a Likbez lecture to plug that hole in their education.
For students' convenience, I shall keep a log of lectures and their subjects on this page. Since the pace of the course may change according to the students' understanding, I will not make a complete schedule at the beginning of the class. Instead, I will simply log every lecture after I give it. This way, if you miss a lecture, you will know what you should read in the textbook and other students' notes.