Matteo Bertolini: Lectures on Supersymmetry

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Supersymmetry    Gauge/String Correspondence
 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 Elementary 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

#### Content

• 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
Vector superfields
• 5. Supersymmetric actions: minimal supersymmetry ( pdf )
N=1 matter actions
Non-linear sigma model I
N=1 SuperYang-Mills
N=1 Gauge-Matter actions
Classical moduli space: examples
The SuperHiggs mechanism
Non-linear sigma model II
• 6. Supersymmetric actions: extended supersymmetry ( pdf )
N=2 supersymmetric actions
Non-linear sigma model III
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
Supersymmetry breaking and spontaneously broken global symmetries
Topological constraints: the Witten index
Genericity and metastability
• 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
Gravity mediation
Gauge mediation
• 9. Non-perturbative effects and holomorphy ( pdf )
Instantons and anomalies in a nutshell
t'Hooft anomaly matching condition
Holomorphy
Holomorphy and non-renormalization theorems
Holomorphic decoupling
• 10. Supersymmetric gauge dynamics: N=1 ( pdf )
On confinement in QCD, YM and SYM theories
Phases of gauge theories: examples
N=1 SQCD: classical analysis
Pure SYM: gaugino condensation
SQCD for N_f < N_c: the ADS superpotential
Integrating in and out: the linearity principle
SQCD for N_f=N_c and N_f=N_c+1
Conformal window
Electric-magnetic (aka Seiberg) duality
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
Metastable SUSY breaking vacua in massive SQCD
Summary of basic results
Massive SQCD in the magnetic-free phase: electric description
Massive SQCD in the magnetic-free phase: magnetic description
Summary of the physical picture