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Supersymmetry as a theoretical laboratory
Study supersymmetric algebras and field theories as controlled theoretical frameworks, explicitly separating mathematical predictions from experimental confirmation.
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Module 01 research
Supersymmetry as a theoretical laboratory
Study supersymmetric algebras and field theories as controlled theoretical frameworks, explicitly separating mathematical predictions from experimental confirmation.
- 01
Super-Poincaré algebra and representation multiplets
Fix spinor and supercharge conventions, construct finite massive multiplets, and obtain a central-charge bound from positivity.
30 min - 02
Supersymmetric quantum mechanics and the Witten index
Factor partner Hamiltonians, identify normalizable zero modes, and state the spectral and boundary assumptions behind an index argument.
28 min - 03
Four-dimensional chiral supermultiplets
Match chiral component transformations and degrees of freedom, then eliminate the auxiliary field without changing the physical particle count.
29 min - 04
Superspace and superfield components
Use ordered Grassmann coordinates and normalized Berezin measures to extract chiral components and construct supersymmetric actions.
30 min - 05
Wess-Zumino model and superpotentials
Derive a scalar potential and Yukawa coupling from one holomorphic function and distinguish vacuum masses from background coefficients.
29 min - 06
Supersymmetric gauge actions and D terms
Normalize a vector multiplet and its matter couplings, eliminate the real auxiliary D, and distinguish gauge fixing from physical polarization counting.
29 min - 07
F- and D-flat vacuum moduli
Solve zero-potential conditions before quotienting gauge orbits and identify which continuous vacuum parameters survive an added superpotential.
29 min - 08
Holomorphy and nonrenormalization theorems
State the Wilsonian perturbative theorem with its hypotheses and distinguish protected holomorphic couplings from running canonically normalized observables.
30 min - 09
Supersymmetry breaking and the Goldstino
Diagnose spontaneous rigid supersymmetry breaking in a stable toy vacuum and distinguish its Goldstino from a pseudomodulus or an explicit mass splitting.
30 min - 10
Seiberg duality and matching tests
Compare electric and magnetic SQCD descriptions through global charges, anomalies, operator maps and deformations while separating evidence from a general proof.
30 min