PHY 880 - Introduction to supersymmetric field theories (Fall 2005)

Instructor

Nicolas Chatillon
Physics Building, Office 369
(315) 443-3895
nchatill[at]physics.syr.edu

Office hours

Come and see me when you want !

Time and Location

Tuesdays and Thursdays from 9:30am till 10:50am. Physics Building 105. First class: Tuesday, August 30.

Contents (evolving)

Supersymmetry, a symmetry between particles of integer and half-integer
spins, is often considered to be the ultimate symmetry of Nature. It is,
among other applications, at the heart of one of the most popular
extensions of the Standard Model of particle physics. Its
non-renormalization properties make it an excellent laboratory for
controlling quantum calculations in field theories, and allows one to
solve the gauge naturalness problem of the standard model. Its local
version, supergravity, makes contact, very elegantly, with Einstein
gravity, and is the form of most of the superstring effective field
theories.

This graduate course will cover the basic formalism of supersymmetry, as
well as one of its applications to particle physics beyond the standard model, in
the form of the supersymmetric standard model. Supergravity and SUSY breaking
models should be discussed too.

Necessary preliminary tools, such as scalar and Dirac field theory, gauge theories, Feynman
graphs and the standard model of particle physics, will be quickly introduced depending on
students background.

1) Why supersymmetry ? (class 1)

2) Lorentz group representations, Dirac and Weyl spinors (class 2-3)

SO(3) and SO(3,1) representations, Dirac equation, Clifford algebra, Weyl spinors ;
comments on spin-statistics theorem and parity violation.

References :
- beginning of H.J.W. Muller-Kirsten and A. Wiedemann, Supersymmetry, an introduction with conceptual and calculational details (library ref. QC 174.17 S9 S85)
for Lorentz group representations
- Fuchs and Schweigert, Symmetries, Lie algebras and representations (library ref QC 20.7 L54 F83)
for background generalities on group theory for physicists if you don't feel comfortable with this.

3) Simple SUSY algebra (class 3-4)

Coleman-Mandula and HLS theorems for spacetime symmetries,
simple (N=1) supersymmetry algebra.

References : Wess & Bagger, Bailin & Love.

4) Extended and higher-dimensional SUSY algebras (class 4-5)

Extended (N>1) supersymmetry algebra,
higher dimensional spinors, R-symmetry, central charges.

References : Wess & Bagger, Bailin & Love,
sections 3 and 4 of Y. Tanii, Introduction to supergravities in diverse dimensions, hep-th/9802138, for higher dimensional spinors and R-symmetry groups.

5) Chiral superfields : SUSY matter (class 6-7-8-9)

Grassmann variables, N=1 superspace, general superfields, component expansion ;
definition of chiral superfields, supersymmetric actions, superpotential, Kahler potential, Kahler geometry ;
F-term spontaneous SUSY breaking, O'Raifeartaigh model.

References : Wess & Bagger, Bailin & Love ;
For people interested in mathematical foundations of Grassmann algebra : Buchbinder & Kuzenko, Ideas and methods of supersymmetry and supergravity (published by IOP).

6) Vector superfields : SUSY gauge fields (class 9-10)

Definition, SUSY gauge invariance, supersymmetric actions,
Fayet-Iliopoulos terms, D-term spontaneous SUSY breaking, non-abelian case.

References : Wess & Bagger, Bailin & Love, Lykken hep-th/9612114.

7) Brief introduction to quantum field theory (class 11-14)

Motivations, scalar field canonical quantization, particle interpretation, S matrix,
perturbative expansion, propagators, Wick theorem, Feynman graphs,
principles of perturbative renormalization.

8) Supersymmetry and renormalization (class 14-17)

Feynman rules in SUSY, mass renormalization, effective field theories and naturalness,
SUSY cancellation of quadratic divergences.

9) Minimal SUSY standard model (MSSM) (class 18-19)

Minimal field content, superpotential, R-parity, soft SUSY breaking sector.

10) MSSM properties and problems (class 20-22)

Hierarchy problem, gauge coupling unification, modified electroweak symmetry breaking,
dark matter candidate(s).
Flavour and CP problems, mu problem, next-to-minimal SUSY standard model.

11) Local supersymmetry : supergravity (SUGRA) (class 22-24)

Vielbein and spin connection, gravitino field,
Noether method for local supersymmetrization, Kahler potential and matter coupled SUGRA.

12) SUSY breaking models (class 24-25)

Super-Higgs effect, Polonyi model, general gravity-mediated SUSY breaking.

Homework

Homework exercices (not graded) will be proposed by the instructor.

Exam

It will be a take-home exam two weeks before the end of the course containing
questions close to the course content and wider problems. Discussions between
students are authorized.

Exam deadline : December 16.

Literature

We will not follow a specific book for all the course (the Bailin & Love sometimes) but these are suggestions :

• D. Bailin & A. Love, Supersymmetric Gauge Field Theory and String Theory. A rather easy reading one. First 80 pages (on 320) focus on global SUSY, then pages 83-149 focus on supergravity action building and model building, and the rest is about string theory. We should talk mostly about the global SUSY part and supergravity in the course, not about strings. The minimal SUSY standard model is not discussed much in the book. There may be some typos in the formulas.

• J. Wess & J. Bagger : Supersymmetry and Supergravity. A standard SUSY textbook. The global SUSY part (about one half) is similar to Bailin & Love, and also introduces supergraphs, but does not discuss SUSY standard model. The supergravity part (last half) is introduced through curved superspace and is rather technical, we will not use this formalism.

• Srivastava, Supersymmetry, superfields and supergravity : an introduction (library ref. QC 174.17 S9 S75). Another good introductory book with a global SUSY part similar to the previous two books, a more detailled discussion of supergraphs and a small supergravity part.

• S. Weinberg, The Quantum Theory of Fields volume III : Supersymmetry. A more complete SUSY book with a variety of subjects. There is a small supergravity part at the end.

Some pedagogical arxiv reviews focused on SUSY formalism and the SUSY standard model :

• S.P. Martin, A Supersymmetry Primer, hep-ph/9709356,
• M. Drees, An Introduction to Supersymmetry, hep-ph/9611409,
• J.D. Lykken, Introduction to Supersymmetry, hep-th/9612114.

Web page last updated December 8, 2005 by N. Chatillon.