DEPARTMENT OF PHYSICS AND ASTRONOMY -- (202) 806-6245 (main office), -5830 (fax)

Theoretical Physics 2 (216-239-01) MW 3⁰⁰-4³⁰ pm;
Office hrs.: MW 3 - 5, and by appointment (at least one day ahead, confirmed)
[Topics][Daily Schedule][Assignments][Welcome]

Instructor: Tristan Hübsch (Office hours: Tue., 1⁰⁰ - 3⁰⁰ & by appointment, at least a day ahead)

TKH#213, 806-6267 thubsch@mac.com

Textbook (required): J.Wess and J.Bagger: Supersymmetry and Supergravity

(opt.): P.West: Introduction to Supersymmetry and Supergravity
(opt.): I.L.Buchbinder and S.M.Kuzenko: Ideas and Methods of Supersymmetry and Supergravity : Or a Walk Through Superspace
(opt.): H.Muller-Kirsten, A.Wiedmann: Supersymmetry : An Introduction With Conceptual and Calculational Details (sadly, out of print)
(opt.): S.J.Gates, Jr. et al.: Superspace or 1001 Lessons in Supersymmetry (sadly, out of print)
--- and several other sources, as given in class

Component	Due time	Remark	% of Grade
Homework	See in daily schedule	Late HW = 0 credit !!!	3 x 20%
Term project and presentation	End of class	25 min. + 10 min. questions	40%

The aim of the course is to give a brief but uncompromising introduction to supersymmetry, both global (rigid) and local (supergravity). We begin with reviewing the motivation for considering supersymmetry, and then proceed by studying the simplest (and most often used) supersymmetric models. The first part of the course considers only global (rigid) supersymmetry, i.e.., supersymmetry in flat spacetime. The second part introduces supergravity: the fully dynamical theory of local supersymmetry which induces and generalizes gravity.

A successful student is expected to demonstrate a very good understanding of the fundamental principles of supersymmetric quantum field theory, but also to demonstrate-and maintain-the ability to solve practical problems involving quantum superfields.

Topical schedule:

Part I:Supersymmetry

• Why Supersymmetry?
• Representations of the Super Symmetry Algebra
• Component Fields vs. Superfields
• Scalar and Vector Superfields, Gauge Invariant Interactions
• Spontaneous Supersymmetry Breaking
• Superfield Propagators, Feynman Rules for Supergraphs
• Differential Forms in Superspace, Gauge Theories Revisited

Part II: Supergravity

• Vielbein, Torsion and Curvature, Bianchi Identities
• Supergauge Transformations
• The Supergravity Multiplet
• Superfields in Curved (Super)Spacetime
• Invariant Lagrangians

Part III: Further topics

• Applications to model building
• 2-dimensional theories

Day-to-day schedule: Students are required to read ahead and discuss in class!

Last year's schedule; will be modified soon.

1/08: Introductory matters
1/11: Why supersymmetry? §1
1/13: The Coleman-Mandula Theorem and the Haag-Lopusanski-Sohnius Theorem. §1
1/15: Representations of supersymmetry §2
1/18: Observed holiday: Martin Luther King's birthday
1/20: Component fields §3
1/22: Superfields -- the general idea §4[HW1 due]
1/25: Chiral superfields §5
1/27: Chiral superfields as superconstrained superfields (extra)
1/29: Vector superfields: the constrained superfield §6
2/01: Vector superfields: gauge transformations and the Wess-Zumino gauge §6
2/03: Gauge invariant interactions §7
2/05: U(1) Gauge invariant interactions and R-transformations (extra)[HW2 due]
2/08: Spontaneous supersymmetry breaking §8
2/10: Spontaneous symmetry breaking §8
2/12: Superfield propagators: component field derivation §9
2/15: Observed Holiday: President's day
2/17: Superfield propagators :the full superfield result §9
2/19: Superfield propagators: projectors §9 [HW3 due]
2/22: Supergraphiti: path integrals and n-point functions §10
2/24: Supergraphiti: Feynman rules for 1PI diagrams §10
2/26: Differential forms in superspace: basic definitions §12
3/01: Differential forms in superspace: general covariance and Yang-Mills covariance §12
3/03: Flat super-Yang-Mills theories §13
3/05: Flat super-Yang-Mills Lagrangians and equations of motion §13[HW4 due]
3/08: Supergravity: gauged supersymmetry §14
3/10: Bianchi identities: geometrical meaning §15
3/12: Bianchi identities: solutions §15
3/15: Supergauge theories §16
3/17: Dynamical fields in the vielbein, torsion and curvature §17
3/19: The supergravity multiplet §18 [HW5 due]
--Spring recess: March 19th, close of classes--29th, 8:00 a.m.
3/29: Constrained superfields in curved (super)spacetime §19
3/31: Invariant Lagrangians §21
4/02: Model building: mass-terms and the Standard model (extra)
4/05: Model building: modification of the RGEs and Grand Unification (extra)
4/07: 2-dimensional spacetime: SO(1,1) as the Lorentz group (extra)
4/09: 2-dimensional spacetime: constrained superfields (extra)
4/12: 2-dimensional spacetime: admissible supersymmetric Lagrangian densities (extra)
4/14: 2-dimensional spacetime: unidexterous superfields (extra)
4/16: presentations and discussion
4/19: presentations and discussion
4/21: presentations and discussion

Homework assignments

1. Due 1/22: 1.1, 1.2, 2.1, 2.2
2. Due 2/05: 3.1, 3.3, 3.4, 4.5, 4.6, 5.4, 5.5
3. Due 2/19: 6.1, 6.3, 7.2, 7.3, 7.7, 8.2, 8.4
4. Due 3/05: 9.1, 9.2, 9.4, 10.1, 10.7, 12.3, 12.9
5. Due 3/19: 13.3, 13.5, 13.7, 14.3, 15.1, 15.3, 16.1

All homework assignments are due by 5:00 pm of the day indicated and should be either given to the instructor in hand, left in the instructor's mailbox in TKH#105, or slid under the instructor's office door, TKH#213. Late homework will not be accepted, except in cases of proven (medical) emergency.

Collaboration policy
Collaboration -- but not blind copying -- on the homework and term paper assignments is strongly encouraged; students should use this to learn from each other. However, each student must demonstrate a good understanding of the presentation topic - at the presentation. Failure to do so would imply covered under University regulations on academic dishonesty and cheating.

Coursework presentation and organization
While a neat presentation of homework is not required for full credit, it certainly makes it easier to assess the quality of the work and give the proper credit due. In all cases, include a simple sketch if it might help conveying the approach or the calculations. Where necessary, include: all units and complete symbols, such as the precise measure and limits of an integral, etc., and references for all quoted and cited material.

• Homework: Submitted answer sheets should be stapled (preferably in the top-left corner). The Student's full name (and ID number) should be indicated on the first (cover) page. Solutions should be labeled and ordered consecutively by the problem numbers. Include all calculation/work and give full reference to any result quoted from any source other than the text, and page/equation number for results quoted from the text or otherwise.
• Term paper and presentation: Each student will freely choose a topic for the term project from among the chapters in the required text. The project will then consist of exploring the references given in the text, performing sample calculations and writing a 15-20 page review paper. This review will also be presented in a 20-25 minute talk, with a 10-15 minute question period at the end. The students are expected to start on the project at least one month before the end of the due date, and interact with the instructor and among each other as much as possible. The paper and the presentation are expected to be at the professional level.

© Tristan Hübsch, 2000