PHY 621, Fall '10

(Official Course Title: QUANTUM THEORY OF FIELDS)

Lecturer: Finn Larsen


Mon+Wed 9.00-10.30 am, 271 Dennison.
Wed 10.30-12.00, 3481 Randall.
J. Terning, ''Modern Supersymmetry"; Oxford (2009).


This course continues the study of  quantum field theory initiated in PHY 513 and PHY523, by developing theories with supersymmetry.

Theories with supersymmetry are of great theoretical interest because they provide concrete realizations of many phenomena in modern effective quantum field theory, in a setting that would not generally be under control. They also connect well to foundational ideas like super string theory.

Theories with supersymmetry are also an important research area because in some versions they form well motivated and testable benchmarks for particle physics experiments, like those underway at the LHC, and those seeking to elucidate dark matter in the universe. As these experiments progress it will remain of great interest to interpret signatures in the context of supersymmetry.

This course will seek to serve students with "formal" and "phenomenological" interests alike, by providing a common language that can faciliate communication. In other words, the course will not develop concrete models with experimental consequences, nor will it connect to fundamental theory such as string theory. Instead, the purpose is to it develop a theoretical framework that is useful from either perspective.



Lecture 1
Lecture 2
Sep. 6-10
(Labor Day)
The SUSY Algebra (sec 1.1-1.3)

Sep. 13-17
The Wess-Zumino Model (sec 2.1-2.4, A1-A2) Super Yang-Mills Theory (sec 2.5-2.6) HW1.pdf

Sep. 20-24
Super Space (sec 2.7)

The Renormalization Group (sec 3.1-3.3, B1-B2) HW2.pdf

Extra reading: sec 3. of Lykken's TASI 1996 notes.

Sep. 27-Oct. 1
The Super-Higgs Mechanism (sec 3.4-3.5)
SUSY Breaking (sec 5.1, 5.3-4)

Oct. 4-8
The MSSM (sec 4.1-2)
Soft Masses and Spurions (sec 2.8, 5.2, 6.1-2)

Oct. 11-15 
Holomorphy: Chiral Field Theory (sec 8.1, 8.3) Anomalies and Instantons (sec 7.2-5)

Oct. 18-22
(Fall Break)
Holomorphy: Gauge Theory (sec 8.4-5) HW5.pdf
Oct. 25-29
The ADS Superpotential (sec 9.1-4,9.6) The NSVZ Beta-Function (sec 7.6-8, 8.2, 8.6) HW6.pdf
Nov 1-5
Seiberg Duality: SUSY QCD (sec 10.3-6) SUSY QCD at F=N, N+1 (sec 10.3, 10.7-10) HW7.pdf

Nov 8-12
Seiberg Duality: SO(N) (sec 10.1, 11.1-3) Deconfinement (sec 11.4-7)

Nov. 15-19
Dynamical SUSY Breaking I (sec 12) Dynamical SUSY Breaking II (sec 12) HW8.pdf
Nov. 22-26
Meta-Stable SUSY Breaking
Seiberg-Witten Theory I (Sec 13.1-3)

Nov. 29-Dec. 3
Seiberg-Witten Theory II (sec 13.4-5)
Seiberg-Witten Theory III(sec 13.6-7)

Dec. 6-10
Super Conformal Field Theory (sec 14)
Quiver Gauge Theories

HWs for the entire course due on wed. dec. 8
Dec 13-17
Anomaly Mediation
NO CLASS - monday is last day of class.

Final Exam available thu. dec 9., due mon. dec 13.



Each week you should:
1) Read the material indicated in the syllabus above under each of the two lectures. You are supposed to read
ALL the material indicated, also when it was not covered in class. 
2) Check the formulae in the sections you are reading. It is good practice for you to do the algebra. Also, it will often be useful to focus on concepts in class, leaving the computations for homestudy. This puts some responsibility on you, the student.
3) Complete the assigned problems during the week indicated on the syllabus, with virtual due date on the following monday. You are welcome to work together.
4) Submit written solutions to the problems in early december.


The GRADE will tentatively be determined from:
1) Homework (1/2).
2) Final take home exam (1/2).


There are many ressources for learning about supersymmetry.
Each has different emphasis and goals; and readers have different preferences. There is not yet any widely adopted text in the field. Indeed, the "field" of supersymmetry is somewhat divided among phenomenological applications and formal developments. The former is exciting, because it is testable; but it is often unprincipled and poorly motivated. The latter is better in that way because it is grounded in effective quantum field theory and motivated by string theory; but it may be irrelevant as far as current experiments are concerned. The textbook in this course serves both of these perspectives (although the lectures will have a modest "formal" prejudice). In practice most students will focus on one perspective or the other; and then find that more detail is needed. In order to fill this need, here is a (very incomplete list of) ressources that I recommend:

1) J. Wess and J. Bagger, "Supersymmetry".

This is *the* textbook for SUSY formalism. It is *strongly* recommended.

Drawbacks: It is exceptionally terse. It lacks important modern developments.

2) Intriligator and Seiberg: "Lectures on Supersymmetric Gauge Theories and Electro-Magnetic Duality", hep-th/9509066, and "Lectures on Supersymmetry Breaking", hep-th/0702069.

Authoritative lectures by masters of the field. Most subjects of interest for current formal developments are covered. Additionally, these lectures are available for free on the Arxive.

Drawbacks: these are not self-contained in that they require the first ~10 chapters of Wess and Bagger (or equivalent) as background. The relation to phenomenological motivations is marginal.

3) S. Weinberg:"Quantum Theory of Fields, vol III".
A magnificent reference for supersymmetry, both foundations and applications. Very insightful, often original, never incorrect.

Drawbacks: since this is the 3rd volume of a series there is less review of relevant QFT than some other references. Also, a universal complaint is the notation, specifically the use of 4-component spinors.

4) P. Argyres,"Supersymmetry Notes".

A complete and excellent course on supersymmetry. Free on the internet.

Drawback: a "formal" prejudice (phenomenology in passing only, at best). Some modern developments (like dynamical SYSY breaking) are not developed.

5) Binetruy:"Supersymmetry: Theory, Experiment, and Cosmology", Oxford (2006).

A full monograph, at a high level (for phenomenology). Detailed signatures for colliders and cosmology.

Drawback: little development of formal background. Focus on "generic" and/or "popular" models.

6) Baer and Tata: "Weak Scale Supersymmetry: from Supefields to Scattering Events".

Modern introduction to supersymmetry phenomonology, with emphasis on colliders.

Drawback: introductory level.

7) M. Luty: "2004 TASI lectures on supersymmetry breaking", hep-th/0509029.

Discussion of the pros and cons of supersymmetry from a modern effective field theory point of view. Highly recommended.

8) J. D. Lykken: "Introduction to Supersymmetry." TASI 1996. hep-th/9612114.

Short introduction to the formalism of supersymmetry. A good reference for self-study prior to the start of the course.