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Dynamics of SUSY gauge theories in four dimensions

Gabriele Ferretti - Chalmers University of Technology, Goteborg


In these lectures I will present some aspects of N=1 rigid SUSY theories in four dimensions that have become standard material in the curriculum of theoretical physics. We will start with a short ``reality check" to get an idea of the level of the audience, followed by an Introduction that can vary between 20 min. or 2 hrs depending on the outcome.

We then move on to the core material. I divided the lectures into two main blocks: A) unbroken SUSY and B) (spontaneously) broken SUSY. More details are given in the plan on the next page.

Time permitting, in the course of the lectures I will also briefly review some general topics (marked with an * in the plan) that have a broader application. The plan is probably overly optimistic! We will adjust it as we go along but generally I prefer to cover less material than rush through to get to the end.

I do not give directly references to the original work, but instead list some of the most relevant reviews from which the original work can be easily found. For instance you will soon find out that the names of Seiberg and Witten recur quite often...

I will also prepare some problems to help you delve more deeply into the material. Discuss the material and the problems amongst your colleagues and with me as much as you can!

  The plan of the course is:  
    Reality check followed by an Introduction.
    Part A: Unbroken SUSY.
  • Classical moduli space of vacua, with examples.
  • Quantum corrections, what do they mean?
  • Anomalies (*).
  • Super QCD for various numbers of flavors and colors.
  • The large N_c limit (*).
    1. Part B: Broken SUSY
  • Spontaneous SUSY breaking.
  • The supercurrent and the Goldstino.
  • Classical SUSY breaking.
  • Coleman Weinberg Potential (*).
  • Dynamical SUSY breaking and the Witten Index.
  • SUSY quantum mechanics (*).
  • Examples of stable and metastable dynamical SUSY breaking in four dimensions.
      Lecture notes:
    Introduction    Part A    Part B    Problem set
    Here are some of the standard books that can be consulted when learning SUSY. Wess and Bagger has become the trendsetter when it comes to notation, so if you have to brush up on the superspace formalism you better do it there.
      J. Wess, J. Bagger Supersymmetry and supergravity, (Princeton University Press, 1992)
      P.C. West, Introduction to supersymmetry and supergravity (World Scientific, 1999)
      S. Weinbger, The Quantum Theory of Fields. Vol. 3: Supersymmetry (Cambridge University Press, 2000)
      J. Terning, Modern supersymmetry: Dynamics and duality (Oxford University Press)
      On-line reviews:
    This is a list of reviews that discuss the material closest to the one covered in these lectures. Note that the list does not include reviews on phenomenology (MSSM, mediation of SUSY breaking...), extended SUSY (N=4 SUSY, S-duality, integrability, N=2 Seiberg-Witten solution...), AdS/CFT related subjects (SCFT, Duality cascades...), supergravity, strings, branes...
    The reviews below are ordered roughly by the same order in which the topics are presented in the lectures.
      J.D. Lykken Introduction to supersymmetry, hep-th/9612114
      A. Bilal, Introduction to supersymmetry hep-th/0101055
      J.M. Figueroa-O'Farrill, Busstepp lectures on supersymmetry hep-th/0109172
      R. Argurio, G. Ferretti, R. Heise, An Introduction to supersymmetric gauge theories and matrix models Int. J. Mod. Phys. A19 (2004) 2015 [hep-th/0311066]
      M.A. Shifman, Nonperturbative dynamics in supersymmetric gauge theories Prog. Part. Nucl. Phys. 39 (1997) 1 [hep-th/9704114]
      K.A. Intriligator, N. Seiberg, Lectures on supersymmetric gauge theories and electric-magnetic duality Nucl. Phys. Proc. Suppl. 45BC (1996) 1 [hep-th/9509066]
      M.E. Peskin, Duality in supersymmetric Yang-Mills theory hep-th/9702094.
      E. Poppitz, S.P. Trivedi, Dynamical supersymmetry breaking Ann. Rev. Nucl. Part. Sci. 48 (1998) 307 [hep-th/9803107]
      K.A. Intriligator, N. Seiberg, Lectures on Supersymmetry Breaking Class. Quant. Grav. 24 (2007) S741 [hep-ph/0702069]
      On-line lecture notes:
    Lastly, here are links to some nice online lecture notes that I consulted when preparing the lectures.
      P. Argyres
      R. Argurio
      M. Bertolini