Matteo Bertolini: Lectures on Supersymmetry SISSA Home

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Susy picture
Every particle has its partner... (from CERN site)

" Darn! Almost got it!"

      -- Albert Einstein

I teach a one-semester graduate course on (rigid) SUPERSYMMETRY to students attending the Theoretical Particle Physics PhD curriculum at SISSA. Below you can find the index of the topics discussed, a big file containing the full set of lectures as well as separate pdf files for each lecture.

Disclaimer. These notes are rather preliminary in many aspects, and permanently work in progress. Moreover, there might be many small mistakes and typos. I hope to be able to improve them in the near future. Any suggestions or comments in this direction are most welcome.

Lectures on Supersymmetry PDF


  • 1 Supersymmetry: a bird's eye view ( pdf )
    What is supersymmetry?
    What is supersymmetry useful for?
  • 2. The Supersymmetry algebra ( pdf )
    Lorentz and Poincare' groups
    Spinors and representations of the Lorentz group
    The supersymmetry algebra
  • 3. Representations of the Supersymmetry algebra ( pdf )
    Massless supermultiplets
    Massive supermultiplets
    Representation on fields: a first try
  • 4. Superspace and Superfields ( pdf )
    Superspace as a coset
    Superfields as fields in superspace
    On supersymmetric invariant actions
    Chiral superfields
    Real superfields
    Current superfields
  • 5. Supersymmetric actions: minimal supersymmetry ( pdf )
    N=1 matter actions
    N=1 SuperYang-Mills
    N=1 Gauge-Matter actions
  • 6. Supersymmetric actions: extended supersymmetry ( pdf )
    N=2 supersymmetric actions
    N=4 supersymmetric actions
    Non-renormalization theorems
  • 7. Supersymmetry breaking ( pdf )
    Vacua in supersymmetric theories
    The goldstone theorem and the goldstino
    F-term breaking
    Pseudomoduli space: quantum corrections
    D-term breaking
    Indirect criteria for supersymmetry breaking
  • 8. Mediation of supersymmetry breaking ( pdf )
    Towards dynamical supersymmetry breaking
    The Supertrace mass formula
    Beyond Minimal Supersymmetric Standard Model
    Spurion fields, soft terms and the messenger paradigm
    Mediating the breaking
  • 9. Non-perturbative effects and holomorphy ( pdf )
    Instantons and anomalies in a nutshell
    t'Hooft anomaly matching condition
    Holomorphy and non-renormalization theorems
    Holomorphic decoupling
  • 10. Supersymmetric gauge dynamics: N=1 ( pdf )
    Confinement in QCD, YM and SYM theories
    Phases of gauge theories: examples
    N=1 SQCD: perturbative analysis
    N=1 SQCD: non-perturbative dynamics
    The phase diagram of N=1 SQCD
  • 11. Dynamical supersymmetry breaking ( pdf )
    Calculable and non-calculable models: generalities
    The one GUT family SU(5) model
    The 3-2 model: instanton driven supersymmetry breaking
    The 4-1 model: gaugino condensation driven supersymmetry breaking
    The ITIY model: supersymmetry breaking with classical flat directions
    DSB into metastable vacua. A case study: massive SQCD
  • 12. Supersymmetric gauge dynamics: extended supersymmetry ( pdf )
    Low energy effective actions: classical and quantum
    Monopoles, dyons and electric-magnetic duality
    Seiberg-Witten theory
    N=4: Montonen-Olive duality

Supersymmetry on the Web (Lecture notes)

Advanced Supersymmetry (duality and alike) on the Web